Abstract

Lidar is a powerful active remote sensing device used in the detection of the optical properties of aerosols and clouds. However, there are difficulties in layer detection and classification. Many previous methods are too complex for large dataset analysis or limited to data with too high a signal-to-noise ratio (SNR). In this study, a mechanism of multiscale detection and overdetection rejection is proposed based on a trend index function that we define. Finally, we classify layers based on connected layers employing a quantity known as the threshold of the peak-to-base ratio. We find good consistency between retrieved results employing our method and visual analysis. The testing of synthetic signals shows that our algorithm performs well with SNRs higher than 4. The results demonstrate that our algorithm is simple, practical, and suited to large dataset applications.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (4)

W. Gong, F. Mao, and S. Song, “Signal simplification and cloud detection with an improved Douglas–Peucker algorithm for single-channel lidar,” Meteorol. Atmos. Phys. 113, 89–97(2011).
[CrossRef]

W. Gong, F. Mao, and J. Li, “OFLID: simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284, 2966–2971 (2011).
[CrossRef]

Y. Ma, W. Gong, P. Wang, and X. Hu, “New dust aerosol identification method for spaceborne lidar measurements,” J. Quant. Spectrosc. Radiat. Trans. 112, 338–345 (2011).
[CrossRef]

W. Gong, J. Li, F. Mao, and J. Zhang, “Comparison of simultaneous signals obtained from a dual-field-of-view lidar and its application to noise reduction based on empirical mode decomposition,” Chin. Opt. Lett. 9, 050101 (2011).
[CrossRef]

2010 (1)

F. Mao, W. Gong, J. Li, and J. Zhang, “Cloud detection and coefficient retrieve based on improved differential zero-crossing method for Mie lidar,” Acta Opt. Sin. 30, 3097–3102(2010).
[CrossRef]

2007 (3)

A. Ben-David, C. E. Davidson, and R. G. Vanderbeek, “Lidar detection algorithm for time and range anomalies,” Appl. Opt. 46, 7275–7288 (2007).
[CrossRef] [PubMed]

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, “STRAT: an automated algorithm to retrieve the vertical structure of the atmosphere from single-channel lidar data,” J. Atmos. Ocean. Technol. 24, 761–775 (2007).
[CrossRef]

2005 (2)

V. A. Kovalev, J. Newton, C. Wold, and W. M. Hao, “Simple algorithm to determine the near-edge smoke boundaries with scanning lidar,” Appl. Opt. 44, 1761–1768 (2005).
[CrossRef] [PubMed]

G. Ohring, B. Wielicki, R. Spencer, B. Emery, and R. Datla, “Satellite instrument calibration for measuring global climate change,” Bull. Am. Meteor. Soc 86, 1303–1313 (2005).
[CrossRef]

2004 (2)

Q. Min, P. Minnis, and M. M. Khaiyer, “Comparison of cirrus optical depths derived from GOES 8 and surface measurements,” J. Geophys. Res. 109, D15207 (2004).
[CrossRef]

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

2003 (1)

D. M. Winker, J. R. Pelon, and M. P. McCormick, “The CALIPSO mission: spaceborne lidar for observation of aerosols and clouds,” Proc. SPIE 4893, 1–11 (2003).
[CrossRef]

2001 (3)

E. J. Welton, J. R. Campbell, J. D. Spinhirne, and S. Stanley, “Global monitoring of clouds and aerosols using a network of micro-pulse lidar systems,” Proc. SPIE 4153, 151–158 (2001).
[CrossRef]

Z. Wang and K. Sassen, “Cloud type and macrophysical property retrieval using multiple remote sensors,” J. Appl. Meteorol. 40, 1665–1682 (2001).
[CrossRef]

D. E. Day and W. C. Malm, “Aerosol light scattering measurements as a function of relative humidity: a comparison between measurements made at three different sites,” Atmos. Environ. 35, 5169–5176 (2001).
[CrossRef]

1994 (1)

D. M. Winker and M. A. Vaughan, “Vertical distribution of clouds over Hampton, Virginia observed by lidar under the ECLIPS and FIRE ETO programs,” Atmos. Res. 34, 117–133(1994).
[CrossRef]

1992 (1)

1989 (1)

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Ahmad, E.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Aoki, K.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

Arao, K.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

Barkstrom, B. R.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Ben-David, A.

BenZvi, S. Y.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Campbell, J. R.

E. J. Welton, J. R. Campbell, J. D. Spinhirne, and S. Stanley, “Global monitoring of clouds and aerosols using a network of micro-pulse lidar systems,” Proc. SPIE 4153, 151–158 (2001).
[CrossRef]

Carswell, A. I.

Cess, R. D.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Cester, R.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Chiosso, M.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Connolly, B. M.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Datla, R.

G. Ohring, B. Wielicki, R. Spencer, B. Emery, and R. Datla, “Satellite instrument calibration for measuring global climate change,” Bull. Am. Meteor. Soc 86, 1303–1313 (2005).
[CrossRef]

Davidson, C. E.

Day, D. E.

D. E. Day and W. C. Malm, “Aerosol light scattering measurements as a function of relative humidity: a comparison between measurements made at three different sites,” Atmos. Environ. 35, 5169–5176 (2001).
[CrossRef]

Drobinski, P.

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, “STRAT: an automated algorithm to retrieve the vertical structure of the atmosphere from single-channel lidar data,” J. Atmos. Ocean. Technol. 24, 761–775 (2007).
[CrossRef]

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar: Theory, Practice, and Analysis Methods (Wiley-Interscience, 2004).
[CrossRef]

Emery, B.

G. Ohring, B. Wielicki, R. Spencer, B. Emery, and R. Datla, “Satellite instrument calibration for measuring global climate change,” Bull. Am. Meteor. Soc 86, 1303–1313 (2005).
[CrossRef]

Filipi, A.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Garcia, B.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Gong, W.

W. Gong, F. Mao, and J. Li, “OFLID: simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284, 2966–2971 (2011).
[CrossRef]

Y. Ma, W. Gong, P. Wang, and X. Hu, “New dust aerosol identification method for spaceborne lidar measurements,” J. Quant. Spectrosc. Radiat. Trans. 112, 338–345 (2011).
[CrossRef]

W. Gong, F. Mao, and S. Song, “Signal simplification and cloud detection with an improved Douglas–Peucker algorithm for single-channel lidar,” Meteorol. Atmos. Phys. 113, 89–97(2011).
[CrossRef]

W. Gong, J. Li, F. Mao, and J. Zhang, “Comparison of simultaneous signals obtained from a dual-field-of-view lidar and its application to noise reduction based on empirical mode decomposition,” Chin. Opt. Lett. 9, 050101 (2011).
[CrossRef]

F. Mao, W. Gong, J. Li, and J. Zhang, “Cloud detection and coefficient retrieve based on improved differential zero-crossing method for Mie lidar,” Acta Opt. Sin. 30, 3097–3102(2010).
[CrossRef]

Grillo, A.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Guarino, F.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Haeffelin, M.

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, “STRAT: an automated algorithm to retrieve the vertical structure of the atmosphere from single-channel lidar data,” J. Atmos. Ocean. Technol. 24, 761–775 (2007).
[CrossRef]

Hao, W. M.

Harrison, E. F.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Hartmann, D.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Horvat, M.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Hu, X.

Y. Ma, W. Gong, P. Wang, and X. Hu, “New dust aerosol identification method for spaceborne lidar measurements,” J. Quant. Spectrosc. Radiat. Trans. 112, 338–345 (2011).
[CrossRef]

Iarlori, M.

S. Y. BenZvi, R. Cester, M. Chiosso, B. M. Connolly, A. Filipi, B. Garcia, A. Grillo, F. Guarino, M. Horvat, and M. Iarlori, “The lidar system of the Pierre Auger Observatory,” Nucl. Inst. Methods Phys. Res. A 574, 171–184 (2007).
[CrossRef]

Kagawa, N.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

Khaiyer, M. M.

Q. Min, P. Minnis, and M. M. Khaiyer, “Comparison of cirrus optical depths derived from GOES 8 and surface measurements,” J. Geophys. Res. 109, D15207 (2004).
[CrossRef]

Kovalev, V. A.

Li, J.

W. Gong, F. Mao, and J. Li, “OFLID: simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284, 2966–2971 (2011).
[CrossRef]

W. Gong, J. Li, F. Mao, and J. Zhang, “Comparison of simultaneous signals obtained from a dual-field-of-view lidar and its application to noise reduction based on empirical mode decomposition,” Chin. Opt. Lett. 9, 050101 (2011).
[CrossRef]

F. Mao, W. Gong, J. Li, and J. Zhang, “Cloud detection and coefficient retrieve based on improved differential zero-crossing method for Mie lidar,” Acta Opt. Sin. 30, 3097–3102(2010).
[CrossRef]

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation(Academic, 2002).

Ma, Y.

Y. Ma, W. Gong, P. Wang, and X. Hu, “New dust aerosol identification method for spaceborne lidar measurements,” J. Quant. Spectrosc. Radiat. Trans. 112, 338–345 (2011).
[CrossRef]

Malm, W. C.

D. E. Day and W. C. Malm, “Aerosol light scattering measurements as a function of relative humidity: a comparison between measurements made at three different sites,” Atmos. Environ. 35, 5169–5176 (2001).
[CrossRef]

Mao, F.

W. Gong, F. Mao, and J. Li, “OFLID: simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284, 2966–2971 (2011).
[CrossRef]

W. Gong, F. Mao, and S. Song, “Signal simplification and cloud detection with an improved Douglas–Peucker algorithm for single-channel lidar,” Meteorol. Atmos. Phys. 113, 89–97(2011).
[CrossRef]

W. Gong, J. Li, F. Mao, and J. Zhang, “Comparison of simultaneous signals obtained from a dual-field-of-view lidar and its application to noise reduction based on empirical mode decomposition,” Chin. Opt. Lett. 9, 050101 (2011).
[CrossRef]

F. Mao, W. Gong, J. Li, and J. Zhang, “Cloud detection and coefficient retrieve based on improved differential zero-crossing method for Mie lidar,” Acta Opt. Sin. 30, 3097–3102(2010).
[CrossRef]

Matsui, I.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

McCormick, M. P.

D. M. Winker, J. R. Pelon, and M. P. McCormick, “The CALIPSO mission: spaceborne lidar for observation of aerosols and clouds,” Proc. SPIE 4893, 1–11 (2003).
[CrossRef]

Min, Q.

Q. Min, P. Minnis, and M. M. Khaiyer, “Comparison of cirrus optical depths derived from GOES 8 and surface measurements,” J. Geophys. Res. 109, D15207 (2004).
[CrossRef]

Minnis, P.

Q. Min, P. Minnis, and M. M. Khaiyer, “Comparison of cirrus optical depths derived from GOES 8 and surface measurements,” J. Geophys. Res. 109, D15207 (2004).
[CrossRef]

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Morille, Y.

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, “STRAT: an automated algorithm to retrieve the vertical structure of the atmosphere from single-channel lidar data,” J. Atmos. Ocean. Technol. 24, 761–775 (2007).
[CrossRef]

Murayama, T.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

Newton, J.

Ohring, G.

G. Ohring, B. Wielicki, R. Spencer, B. Emery, and R. Datla, “Satellite instrument calibration for measuring global climate change,” Bull. Am. Meteor. Soc 86, 1303–1313 (2005).
[CrossRef]

Pal, S. R.

Pelon, J.

Y. Morille, M. Haeffelin, P. Drobinski, and J. Pelon, “STRAT: an automated algorithm to retrieve the vertical structure of the atmosphere from single-channel lidar data,” J. Atmos. Ocean. Technol. 24, 761–775 (2007).
[CrossRef]

Pelon, J. R.

D. M. Winker, J. R. Pelon, and M. P. McCormick, “The CALIPSO mission: spaceborne lidar for observation of aerosols and clouds,” Proc. SPIE 4893, 1–11 (2003).
[CrossRef]

Ramanathan, V.

V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, “Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment,” Science 243, 57–63 (1989).
[CrossRef] [PubMed]

Reba, M. N. M.

F. Rocadenbosch, M. Sicard, M. N. M. Reba, and S. Tomas, “Morphological tools for range-interval segmentation of elastic lidar signals,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2007), pp. 4372–4375.
[CrossRef]

Rocadenbosch, F.

F. Rocadenbosch, M. Sicard, M. N. M. Reba, and S. Tomas, “Morphological tools for range-interval segmentation of elastic lidar signals,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2007), pp. 4372–4375.
[CrossRef]

Sassen, K.

Z. Wang and K. Sassen, “Cloud type and macrophysical property retrieval using multiple remote sensors,” J. Appl. Meteorol. 40, 1665–1682 (2001).
[CrossRef]

Shimizu, A.

A. Shimizu, N. Sugimoto, I. Matsui, K. Arao, I. Uno, T. Murayama, N. Kagawa, K. Aoki, A. Uchiyama, and A. Yamazaki, “Continuous observations of Asian dust and other aerosols by polarization lidars in China and Japan during ACE-Asia,” J. Geophys. Res. 109, D19S17 (2004).
[CrossRef]

Sicard, M.

F. Rocadenbosch, M. Sicard, M. N. M. Reba, and S. Tomas, “Morphological tools for range-interval segmentation of elastic lidar signals,” in IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2007), pp. 4372–4375.
[CrossRef]

Song, S.

W. Gong, F. Mao, and S. Song, “Signal simplification and cloud detection with an improved Douglas–Peucker algorithm for single-channel lidar,” Meteorol. Atmos. Phys. 113, 89–97(2011).
[CrossRef]

Spencer, R.

G. Ohring, B. Wielicki, R. Spencer, B. Emery, and R. Datla, “Satellite instrument calibration for measuring global climate change,” Bull. Am. Meteor. Soc 86, 1303–1313 (2005).
[CrossRef]

Spinhirne, J. D.

E. J. Welton, J. R. Campbell, J. D. Spinhirne, and S. Stanley, “Global monitoring of clouds and aerosols using a network of micro-pulse lidar systems,” Proc. SPIE 4153, 151–158 (2001).
[CrossRef]

Stanley, S.

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Figures (6)

Fig. 1
Fig. 1

(a) Ideal range-corrected lidar signal and (b) a real one. Conventional feature bins of a layer (base, top, and peak) are indicated in (a) by the vertical dashed lines. Inset (b), discrete range bins that make up a real lidar signal.

Fig. 2
Fig. 2

Effect of detecting window size on position of layer base. A large window will yield a layer base position indicated by the red circle (left), whereas an “eyeball” estimate is indicated by the orange circle (right).

Fig. 3
Fig. 3

Map of the trend flags for real data. A map of the trend flags is shown in (a), where black and white indicate 1 and 0, respectively, and the window size ranges from 2 to 50. The trend flags shown in the region where the window size is less than zero are the result of multiscale detection. Several interesting regions are circled in red (see text). The resulting classifications are shown in (b), where the original signal is in blue, rejected overdetections are in orange, and range bins in the BPRs of detected layers are red. Regions labeled F and G are small layer regions that were successfully retained by our classification method.

Fig. 4
Fig. 4

Results of tests with different SNR values. Blue denotes the original signal, orange denotes the rejected over detections, and red signifies the accepted detections of the feature region between the layer base and peak.

Fig. 5
Fig. 5

Time-altitude diagrams. (a) Lidar data recorded during a 10 h period in Wuhan, China on 25 December 2008 are shown as ln ( P ( R ) R 2 ) versus altitude and time and (b) corresponding layer detections by our algorithm.

Fig. 6
Fig. 6

Classification results based upon the peak-to-base ratio (a)  ln ( X ) for the signal-by-signal identified layers, (b) flag of detection result obtained with the peak-to-base ratio as shown in (a), (c)  ln ( X ) of the connected layers, and (d) flag of layer detection result obtained with the average X of the connected layers as shown in (c). In (b) and (d), the cloud layers are in red and the aerosol layers are in blue. Several interesting regions are circled in black in (b) and (d) (see text).

Equations (8)

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P ( R ) = 1 R 2 · C · G ( R ) · A · β ( R ) · exp [ 2 0 R α ( R ) d R ] ,
f ( R ) = a + b 0.5 c ,
T c ( R ) = { 1 , if   f ( R ) > 0 0 , others .
P ( R ) = S ( R ) + e ( R ) ,
T ( R ) = { 1 , if   any   T c ( R ) = 1 0 , others .
Δ = P p ( R p ) P b ( R b ) ,
X = P p ( R p ) R p 2 / P b ( R b ) R b 2 ,
X { > 4 , the layer is a cloud layer 4 , the layer is an aerosol layer .

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