Abstract

Fernald method is regarded as the standard method for retrieving lidar data, but the retrieval can be performed only when a boundary value is given. Generally, we can select clear atmosphere above the tropopause as a reference to determine the boundary value, but we need to use the slope method to fit the boundary value when the detecting range is lower than the tropopause. The slope method involves significant uncertainty because this algorithm is based on two hypotheses: one is that aerosol vertical distribution is homogeneous, and the other is that either molecule or aerosol components exist in the atmosphere. To reduce the uncertainty, we proposed a new approach, which segments a signal into “uniform” sub-signals to avoid the first hypothesis, and then uses nonlinear two-component fitting to avoid the second one. Compared with the approach based on the slope method, the new approach obtained more accurate boundary values and retrieving results for both of the simulated and real signals. Thus the automatic segmentation algorithm and the two-component fitting method are useful for determining the reference bin and boundary values when the effective detecting range of lidar is lower than the tropopause.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [PubMed]
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    [Crossref] [PubMed]
  8. F. Mao, W. Gong, and C. Li, “Anti-noise algorithm of lidar data retrieval by combining the ensemble Kalman filter and the Fernald method,” Opt. Express 21(7), 8286–8297 (2013).
    [Crossref] [PubMed]
  9. Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 5(2), 229–241 (1988).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  19. 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(1-2), 88–97 (2011).
    [Crossref]
  20. F. Mao, W. Gong, and T. Logan, “Linear segmentation algorithm for detecting layer boundary with lidar,” Opt. Express 21(22), 26876–26887 (2013).
    [PubMed]
  21. U. NOAA and U. A. Force, “US standard atmosphere,” (1976).
  22. Y. Sasano, “Tropospheric aerosol extinction coefficient profiles derived from scanning lidar measurements over Tsukuba, Japan, from 1990 to 1993,” Appl. Opt. 35(24), 4941–4952 (1996).
    [Crossref] [PubMed]
  23. F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
    [Crossref]

2013 (3)

2012 (1)

2011 (2)

W. Gong, F. Mao, and J. Li, “OFLID: Simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284(12), 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(1-2), 88–97 (2011).
[Crossref]

2010 (2)

2004 (1)

2003 (1)

2000 (1)

1999 (1)

1996 (2)

1993 (1)

1988 (1)

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 5(2), 229–241 (1988).
[Crossref]

1984 (1)

1981 (1)

1973 (1)

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Int. J. Geo. Inf. Geo. 10, 112–122 (1973).

1966 (1)

R. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92(392), 220–230 (1966).
[Crossref]

Albiol, L.

Amodeo, A.

Baldasano, J. M.

Balin, I.

Balis, D.

Bösenberg, J.

Cao, K.

Chaikovsky, A.

Chourdakis, G.

Chu, S.

E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An online algorithm for segmenting time series,” in (Proceedings 2001 IEEE International Conference on Data Mining, 2001), 289–296.
[Crossref]

Collis, R.

R. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92(392), 220–230 (1966).
[Crossref]

Comeron, A.

Comerón, A.

de Leeuw, G.

De Tomasi, F.

Delaval, A.

Douglas, D. H.

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Int. J. Geo. Inf. Geo. 10, 112–122 (1973).

Eixmann, R.

Feiyue, M.

Fernald, F. G.

Freudenthaler, V.

Gong, W.

F. Mao, W. Gong, and C. Li, “Anti-noise algorithm of lidar data retrieval by combining the ensemble Kalman filter and the Fernald method,” Opt. Express 21(7), 8286–8297 (2013).
[Crossref] [PubMed]

F. Mao, W. Gong, and T. Logan, “Linear segmentation algorithm for detecting layer boundary with lidar,” Opt. Express 21(22), 26876–26887 (2013).
[PubMed]

F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
[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(12), 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(1-2), 88–97 (2011).
[Crossref]

Hågård, A.

Hart, D.

E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An online algorithm for segmenting time series,” in (Proceedings 2001 IEEE International Conference on Data Mining, 2001), 289–296.
[Crossref]

Hu, H.

Hu, S.

Jinhuan, Q.

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 5(2), 229–241 (1988).
[Crossref]

Keogh, E.

E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An online algorithm for segmenting time series,” in (Proceedings 2001 IEEE International Conference on Data Mining, 2001), 289–296.
[Crossref]

Klett, J. D.

Komguem, L.

Kovalev, V. A.

Kreipl, S.

Kunz, G. J.

Li, C.

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(12), 2966–2971 (2011).
[Crossref]

Logan, T.

Mao, F.

F. Mao, W. Gong, and T. Logan, “Linear segmentation algorithm for detecting layer boundary with lidar,” Opt. Express 21(22), 26876–26887 (2013).
[PubMed]

F. Mao, W. Gong, and C. Li, “Anti-noise algorithm of lidar data retrieval by combining the ensemble Kalman filter and the Fernald method,” Opt. Express 21(7), 8286–8297 (2013).
[Crossref] [PubMed]

F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
[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(12), 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(1-2), 88–97 (2011).
[Crossref]

Matthais, V.

Matthey, R.

Pazzani, M.

E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An online algorithm for segmenting time series,” in (Proceedings 2001 IEEE International Conference on Data Mining, 2001), 289–296.
[Crossref]

Peucker, T. K.

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Int. J. Geo. Inf. Geo. 10, 112–122 (1973).

Reba, M. N.

Rizi, V.

Rocadenbosch, F.

Rodrigues, J. A.

Sasano, Y.

Sicard, M.

Song, S.

F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
[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(1-2), 88–97 (2011).
[Crossref]

Soriano, C.

Tao, Z.

Wandinger, U.

Wang, X.

Wei, G.

Wu, D.

Yingying, M.

Yuan, K. e.

Zhang, Q.

Zhu, Z.

F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
[Crossref]

Adv. Atmos. Sci. (1)

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 5(2), 229–241 (1988).
[Crossref]

Appl. Opt. (10)

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20(2), 211–220 (1981).
[Crossref] [PubMed]

F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23(5), 652–653 (1984).
[Crossref] [PubMed]

G. J. Kunz and G. de Leeuw, “Inversion of lidar signals with the slope method,” Appl. Opt. 32(18), 3249–3256 (1993).
[Crossref] [PubMed]

G. J. Kunz, “Transmission as an input boundary value for an analytical solution of a single-scatter lidar equation,” Appl. Opt. 35(18), 3255–3260 (1996).
[Crossref] [PubMed]

Y. Sasano, “Tropospheric aerosol extinction coefficient profiles derived from scanning lidar measurements over Tsukuba, Japan, from 1990 to 1993,” Appl. Opt. 35(24), 4941–4952 (1996).
[Crossref] [PubMed]

F. Rocadenbosch, C. Soriano, A. Comerón, and J. M. Baldasano, “Lidar inversion of atmospheric backscatter and extinction-to-backscatter ratios by use of a Kalman filter,” Appl. Opt. 38(15), 3175–3189 (1999).
[Crossref] [PubMed]

F. Rocadenbosch, A. Comerón, and L. Albiol, “Statistics of the slope-method estimator,” Appl. Opt. 39(33), 6049–6057 (2000).
[Crossref] [PubMed]

V. A. Kovalev, “Stable near-end solution of the lidar equation for clear atmospheres,” Appl. Opt. 42(3), 585–591 (2003).
[PubMed]

V. Matthais, V. Freudenthaler, A. Amodeo, I. Balin, D. Balis, J. Bösenberg, A. Chaikovsky, G. Chourdakis, A. Comeron, A. Delaval, F. De Tomasi, R. Eixmann, A. Hågård, L. Komguem, S. Kreipl, R. Matthey, V. Rizi, J. A. Rodrigues, U. Wandinger, and X. Wang, “Aerosol lidar intercomparison in the framework of the EARLINET project. 1. Instruments,” Appl. Opt. 43(4), 961–976 (2004).
[Crossref] [PubMed]

F. Rocadenbosch, M. N. Reba, M. Sicard, and A. Comerón, “Practical analytical backscatter error bars for elastic one-component lidar inversion algorithm,” Appl. Opt. 49(17), 3380–3393 (2010).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

Int. J. Geo. Inf. Geo. (1)

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Int. J. Geo. Inf. Geo. 10, 112–122 (1973).

Meteorol. Atmos. Phys. (1)

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(1-2), 88–97 (2011).
[Crossref]

Opt. Commun. (1)

W. Gong, F. Mao, and J. Li, “OFLID: Simple method of overlap factor calculation with laser intensity distribution for biaxial lidar,” Opt. Commun. 284(12), 2966–2971 (2011).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

F. Mao, W. Gong, S. Song, and Z. Zhu, “Determination of the boundary layer top from lidar backscatter profiles using a Haar wavelet method over Wuhan, China,” Opt. Laser Technol. 49, 343–349 (2013).
[Crossref]

Opt. Lett. (1)

Q. J. R. Meteorol. Soc. (1)

R. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92(392), 220–230 (1966).
[Crossref]

Other (3)

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

U. NOAA and U. A. Force, “US standard atmosphere,” (1976).

E. Keogh, S. Chu, D. Hart, and M. Pazzani, “An online algorithm for segmenting time series,” in (Proceedings 2001 IEEE International Conference on Data Mining, 2001), 289–296.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Flow chart of the lidar data retrieval based on the segmentation algorithm, two-component fitting method, and Fernald method.
Fig. 2
Fig. 2 Simulated signal experiment: (a) Simulated lidar signals and breakpoints produced by the segmentation algorithm. (b) True value (True) and fitted AEC by the slope (i.e. one-component fitting) method (Fit 1) and two-component fitting method (Fit 2), as well as AEC retrieved by Fernald method with the boundary values obtained based on the two-component fitting method (Fernald 1) and the two-component fitting method (Fernald 2), respectively.
Fig. 3
Fig. 3 Fitting accuracy matrix W(R, n) varies with noise level and number of range bins, which is calculated based on 1000 simulations.
Fig. 4
Fig. 4 Measured signal experiment: (a) Measured lidar signals and break bins generated by automatic segmentation algorithm. (b) Aerosol extinction coefficient fitted by the slope method (Fit 1) and segmented two-component fitting method (Fit 2), of which the negative part is not shown. Three profiles of aerosol extinction coefficients retrieved by the Fernald method were based on the boundary value determined by calibrating at 10 km (Ref.), fitted by the slope method (Fernald 1) and the two-component fitting method (Fernald 2), respectively.
Fig. 5
Fig. 5 Aerosol extinction coefficient retrieved by Fernald method and their differences: (a)-(c) are the aerosol extinction coefficient retrieved by the Fernald method based on the boundary value determined by calibrating at 10 km, fitted by the slope method and the two-component fitting method, respectively.(d) is the difference of the retrieved extinction based on the slope method and the reference value. (e) is the same as (d), but for the two-component fitting method.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

P(r)= C r 2 G( r )[ β 1 (r)+ β 2 (r) ]exp{ 2 0 r [ α 1 (r)+ α 2 (r) ]dr }+e( r ),
X( r )=S(r) r 2 +e(r) r 2 ,
d( r )=| X(r)+ X seg (r) |,
P(r)= C r 2 [ β 1 (r) β 2 (r) +1 ] β 2 (r)exp[ -2 r 1 r 2 ( S 1 (r) β 1 (r) β 2 (r) + S 2 ) β 2 (r)dr ],
a=C[ β 1 (r) β 2 (r) +1 ],
b= S 1 (r) β 1 (r) β 2 (r) + S 2 ,
P(r)= a r 2 β 2 (r)exp[ 2b r 1 r 2 β 2 (r)dr ],
Δ= r= r 1 r 2 { P(r) a r 2 β 2 (r)exp[ 2b r 1 r 2 β 2 (r)dr ] } 2 ,
α 1 (r)= S 1 (r) β 1 (r)=( b S 2 ) β 2 (r),
W(R,n)=f( R )h( n ),
β 1 ( i1 )= X( i1 )exp[ A( i1 ) ] X( i ) β( i ) + S 1 { X( i )+X( i1 )exp[ A( i1 ) ] }Δr β 2 ( i1 ),
β 1 ( i+1 )= X( i+1 )exp[ A( i ) ] X( i ) β( i ) S 1 { X( i )+X( i+1 )exp[ A( i ) ] }Δr β 2 ( i+1 ).

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