Abstract

An experimental method for determining the presence and the level of systematic distortions in lidar data is considered. The method has been developed on the basis of two years of field experiments with the Fire Sciences Laboratory elastic scanning lidar. The influence of multiplicative and additive distortion components is considered using numerical experiments and is illustrated with experimental data. The examination method is most applicable for short wavelengths at which the atmospheric molecular component in clear atmospheres is large enough to stabilize the Kano–Hamilton multiangle solution, based on the assumption of horizontal atmospheric homogeneity.

© 2007 Optical Society of America

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References

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  1. V. A. Kovalev, "Distortions of the extinction coefficient profile caused by systematic errors in lidar data," Appl. Opt. 43, 3191-3198 (2004).
    [CrossRef] [PubMed]
  2. V. Simeonov, G. Larcheveque, P. Quaglia, H. van den Bergh, and B. Calpini, "Influence of the photomultiplier tube spatial uniformity on lidar signals," Appl. Opt. 38, 5186-5190 (1999).
    [CrossRef]
  3. R. R. Agishev and A. Comeron, "Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications," Appl. Opt. 41, 7516-7521 (2002).
    [CrossRef]
  4. Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, "Geometrical form factor in the laser radar equation: an experimental determination," Appl. Opt. 18, 3908-3910 (1979).
    [CrossRef] [PubMed]
  5. K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, "Experimental determination of the crossover function in the laser radar equation for days with a light mist," Appl. Opt. 28, 2194-2195 (1989).
    [CrossRef] [PubMed]
  6. V. A. Kovalev and W. E. Eichinger, Elastic Lidar. Theory, Practice, and Analysis Methods (Wiley, 2004).
    [CrossRef]
  7. M. Adam, V. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, "Application of the Kano-Hamilton multiangle inversion method in clear atmospheres," J. Atmos. Ocean. Technol. , in press.
  8. D. N. Whiteman, "Application of statistical methods to the determination of slope in lidar data," Appl. Opt. 15, 3360-3369 (1999).
    [CrossRef]
  9. F. Rocadenbosh, A. Comeron, and L. Albiol, "Statistics of the slope-method estimator," Appl. Opt. 39, 6049-6057 (2000).
    [CrossRef]
  10. S. N. Volkov, B. V. Kaul, and D. I. Shelefontuk, "Optimal method of linear regression in laser remote sensing," Appl. Opt. 41, 5078-5083 (2002).
    [CrossRef] [PubMed]
  11. M. Kano, "On the determination of backscattered and extinction coefficient of the atmosphere by using laser radar," Papers Meteorol. Geophys. 19, 121-129 (1968).
  12. P. M. Hamilton, "Lidar measurement of backscatter and attenuation of atmospheric aerosol," Atmos. Environ. 3, 221-223 (1969).
    [CrossRef]
  13. M. Sicard, P. Chazette, J. Pelon, J. G. Won, and S. C. Yoon, "Variational method for the retrieval of the optical thickness and the backscatter coefficient from multiangle lidar profiles," Appl. Opt. 41, 493-502 (2002).
    [CrossRef] [PubMed]
  14. V. Kovalev, "Determination of slope in lidar data using a duplicate of the inverted function," Appl. Opt. 45, 8781-8789 (2006).
    [CrossRef] [PubMed]

2006 (1)

2004 (1)

2002 (3)

2000 (1)

1999 (2)

1989 (1)

1979 (1)

1969 (1)

P. M. Hamilton, "Lidar measurement of backscatter and attenuation of atmospheric aerosol," Atmos. Environ. 3, 221-223 (1969).
[CrossRef]

1968 (1)

M. Kano, "On the determination of backscattered and extinction coefficient of the atmosphere by using laser radar," Papers Meteorol. Geophys. 19, 121-129 (1968).

Appl. Opt. (10)

Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, "Geometrical form factor in the laser radar equation: an experimental determination," Appl. Opt. 18, 3908-3910 (1979).
[CrossRef] [PubMed]

V. Simeonov, G. Larcheveque, P. Quaglia, H. van den Bergh, and B. Calpini, "Influence of the photomultiplier tube spatial uniformity on lidar signals," Appl. Opt. 38, 5186-5190 (1999).
[CrossRef]

F. Rocadenbosh, A. Comeron, and L. Albiol, "Statistics of the slope-method estimator," Appl. Opt. 39, 6049-6057 (2000).
[CrossRef]

M. Sicard, P. Chazette, J. Pelon, J. G. Won, and S. C. Yoon, "Variational method for the retrieval of the optical thickness and the backscatter coefficient from multiangle lidar profiles," Appl. Opt. 41, 493-502 (2002).
[CrossRef] [PubMed]

S. N. Volkov, B. V. Kaul, and D. I. Shelefontuk, "Optimal method of linear regression in laser remote sensing," Appl. Opt. 41, 5078-5083 (2002).
[CrossRef] [PubMed]

R. R. Agishev and A. Comeron, "Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications," Appl. Opt. 41, 7516-7521 (2002).
[CrossRef]

V. A. Kovalev, "Distortions of the extinction coefficient profile caused by systematic errors in lidar data," Appl. Opt. 43, 3191-3198 (2004).
[CrossRef] [PubMed]

V. Kovalev, "Determination of slope in lidar data using a duplicate of the inverted function," Appl. Opt. 45, 8781-8789 (2006).
[CrossRef] [PubMed]

K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, "Experimental determination of the crossover function in the laser radar equation for days with a light mist," Appl. Opt. 28, 2194-2195 (1989).
[CrossRef] [PubMed]

D. N. Whiteman, "Application of statistical methods to the determination of slope in lidar data," Appl. Opt. 15, 3360-3369 (1999).
[CrossRef]

Atmos. Environ. (1)

P. M. Hamilton, "Lidar measurement of backscatter and attenuation of atmospheric aerosol," Atmos. Environ. 3, 221-223 (1969).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

M. Adam, V. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, "Application of the Kano-Hamilton multiangle inversion method in clear atmospheres," J. Atmos. Ocean. Technol. , in press.

Papers Meteorol. Geophys. (1)

M. Kano, "On the determination of backscattered and extinction coefficient of the atmosphere by using laser radar," Papers Meteorol. Geophys. 19, 121-129 (1968).

Other (1)

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

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Figures (10)

Fig. 1
Fig. 1

Overlap function q(r) (the thick solid curve) and the distortion function D(r) (the thin solid curve) used for the simulations.

Fig. 2
Fig. 2

Functions y(r) obtained in the simulations. Curve 1 shows the function obtained with an ideal lidar with no noise and no signal systematic distortion; Curve 2 is the same but when the signal is corrupted by random noise, the systematic offset B = 1 , and the multiplicative factor D(r), shown in Fig. 1.

Fig. 3
Fig. 3

Profiles of τ ( 0 , h ) derived with the assumed length of the incomplete overlap zone equal to 372   m (empty triangles) and that derived with the length of the zone equal to 600 m (empty squares). The dashed line shows the true profile.

Fig. 4
Fig. 4

Function [ T ( 0 , h ) ] 2 determined with the initially selected length of the incomplete overlap equal to 372 m (the triangular data points) and their linear fit over the low altitudes (the thin solid line). The squared data points and the thick solid line are the same, but calculated using the length of the incomplete overlap equal to 600   m . The dotted line shows the true (model) profile of [ T ( 0 , h ) ] 2 .

Fig. 5
Fig. 5

Empty squares are the retrieved data points of τ ( 0 , h ) , the same as those used when estimating final [ T ( 0 , h ) ] 2 in Fig. 4. The solid curves 1, 2, and 3 show the profiles of τ int ( 0 , h ) calculated with Eq. (13) using η equal to 0.5 , 0.13   km , and 0.8   km 1 , respectively.

Fig. 6
Fig. 6

Profiles of the total extinction-coefficient, κ total ( h ) retrieved from the optical depth profiles given in Fig. 5. The empty squares show the extinction-coefficient profile extracted from τ ( 0 , h ) . The solid curves 1–3 show the profiles of κ total ( h ) extracted from the corresponding profiles 1–3 in Fig. 5. The dotted curve shows the model profile and the solid circle on the horizontal axes shows the reference point κ total ( h = 0 ) .

Fig. 7
Fig. 7

Distortion of τ ( 0 , h ) caused by different systematic offsets in the lidar signals. The dotted curve shows the inverted function when the shifts B j vary over the range between zero and −1, the thin solid curve shows the case when B j vary between zero and + 1.4 , and the thick solid curve shows the case when B j vary between 0.5 and + 0.5 . The dashed line shows the initial model profile of τ ( 0 , h ) .

Fig. 8
Fig. 8

Profiles of τ ( 0 , h ) retrieved with r max = 3500   m (curve 1, shown by the thin solid curve), and 5000   m (curve 2 shown by the empty circles). Dotted line 3 is the true profile.

Fig. 9
Fig. 9

Example of the optical depth profiles extracted from experimental data with the FSL scanning lidar in the vicinity of the I-90 Fire in Montana in August 2005. The dotted curve is the initial profile of τ ( 0 , h ) . The thin solid lines show the profiles of τ min ( 0 , h ) and τ max ( 0 , h ) in the local zones where they differ from each other; the thick curve is the function τ s h ( 0 , h ) .

Fig. 10
Fig. 10

Dependence of ε on h max for the profile of the optical depth τ ( 0 , h ) shown in Fig. 9.

Equations (19)

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P ( r ) = P total ( r ) B G R = C q ( r ) β ( r ) D ( r ) r 2 × exp [ 2 τ ( 0 , r ) ] + B ( r ) ,
y ( r ) = ln [ C β ] + ln q ( r ) + ln D ( r ) + ln [ 1 + B / P ( r ) ] 2 τ ( 0 , r ) .
q eff ( r ) = q ( r ) D ( r ) [ 1 + B / P ( r ) ] .
P j ( h ) ( h / sin φ j ) 2 = [ P j , total ( h ) B G R j ] ( h / sin φ j ) 2 = C q j ( h ) β j ( h ) D j ( h ) exp [ 2 τ j ( 0 , h ) ] × ( 1 + B j / P j ( h ) ) ,
y j ( h ) = ln P j ( h ) ( h / sin φ j ) 2 ,
y j ( h ) = A ( h ) + ln q j , eff ( h ) 2 τ ( 0 , h ) x j .
A ( h ) = ln [ C β ( h ) ] ,
q j , eff ( h ) = q j ( h ) D j ( h ) ( 1 + B j / P j ( h ) ) .
[ T ( 0 , h ) ] 2 = exp [ 2 τ ( 0 , h ) ] .
[ T ( 0 , h ) ] 2 = a + b h
κ total ( h ) = d τ ( 0 , h ) d h = 0.5 b a + b h .
κ total ( h = 0 ) = κ p , neph + κ m ( h = 0 ) .
τ int ( 0 , h ) = κ total ( h = 0 ) η [ 1 exp ( η h ) ] ,
ξ = ( Δ h int ) [ τ ( 0 , h ) τ int ( 0 , h ) ] 2 ,
κ total ( h ) = κ total ( h = 0 ) exp ( η h ) .
τ max ( 0 , h ) = max [ τ ( 0 , h min ) ; τ ( 0 , h min + Δ h d ) ; τ ( 0 , h min + 2 Δ h d ) ;   …   ;   τ ( 0 , h ) ] ,
τ min ( 0 , h ) = min [ τ ( 0 , h ) ; τ ( 0 , h + Δ h d ) ; τ ( 0 , h + 2 Δ h d ) ;   …   ;   τ ( 0 , h max ) ] .
τ s h ( 0 , h ) = 1 2 [ τ min ( 0 , h ) + τ max ( 0 , h ) ] .
ε = h m i n h m a x [ τ m a x ( 0 , h ) τ m i n ( 0 , h ) ] d h 2 h m i n h m a x τ s h ( 0 , h ) d h .

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