Abstract

A new method is considered that can be used for inverting data obtained from a combined elastic–inelastic lidar or a high spectral resolution lidar operating in a one-directional mode, or an elastic lidar operating in a multiangle mode. The particulate extinction coefficient is retrieved from the simultaneously measured profiles of the particulate backscatter coefficient and the particulate optical depth. The stepwise profile of the column-integrated lidar ratio is found that provides best matching of the initial (inverted) profile of the optical depth to that obtained by the inversion of the backscatter-coefficient profile. The retrieval of the extinction coefficient is made without using numerical differentiation. The method reduces the level of random noise in the retrieved extinction coefficient to the level of noise in the inverted backscatter coefficient. Examples of simulated and experimental data are presented.

© 2007 Optical Society of America

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References

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2007 (2)

2006 (2)

2005 (1)

2002 (1)

2000 (1)

1999 (1)

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

1993 (1)

Appl. Opt. (9)

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. (to be published).

Other (2)

M. Pahlow, V. A. Kovalev, A. Ansmann, and K. Helmert, "Iterative determination of the aerosol extinction coefficient profile and the mean extinction-to-backscatter ratio from multiangle lidar data," in Proceedings of the 22nd International Laser Radar Conference, G. Pappalardo and A. Amodeo, eds. (European Space Agency, 2004), pp. 491-494.

V. A. Kovalev, C. Wold, W. M. Hao, and B. Nordgren, "Improved methodology for the retrieval of the particulate extinction coefficient and lidar ratio from the lidar multiangle measurement," in Lidar Technologies, Techniques, and Measurements for Atmospheric Remote Sensing, U. N. Singh, ed., Proc. SPIE 6750, 31-39 (2007).

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Figures (11)

Fig. 1
Fig. 1

Synthetic noise-corrupted optical depth, τ p ( 0 , h ) (thick solid curve), the base function, τ p , b ( 0 , h ) (the open diamonds), and the upper and lower uncertainty boundaries, τ p , u p ( 0 , h ) and τ p , l o w ( 0 , h ) (the dashed curves) versus height.

Fig. 2
Fig. 2

Simplified flow chart for extracting κ p ( h ) .

Fig. 3
Fig. 3

Base profile, τ p , b ( 0 , h ) (the open diamonds) and the corresponding profiles τ p , u p ( 0 , h ) and τ p , l o w ( 0 , h ) (dashed curves), the same curves as those in Fig. 1. The solid triangles show the profile of τ p ( 0 , h ) calculated with S p , j = 8.38 sr, and the solid dots show the profile derived with S p , j 31 sr.

Fig. 4
Fig. 4

Thin solid curve is the model profile of the extinction coefficient used for the simulations. The profile of κ p ( h ) retrieved with the new method is shown as the thick solid curve; the dotted curve shows the extinction coefficient profile calculated using the conventional numerical differentiation with a vertical range resolution of 500   m .

Fig. 5
Fig. 5

Model lidar ratio, S p ( h ) , used for the simulation (the thin solid curve) and the retrieved stepwise column-integrated profile, S p , j (the thick solid lines). The lidar ratio, S p ( h ) , extracted using the extinction coefficient retrieved with the numerical differentiation is shown as the dotted curve.

Fig. 6
Fig. 6

Backscatter coefficient, β p ( h ) , profile in the simulated atmosphere.

Fig. 7
Fig. 7

Profile of the optical depth, τ p ( 0 , h ) , obtained with an artificial lidar (thin dotted curve) and the uncertainty boundaries, τ p , l o w ( 0 , h ) and τ p , u p ( 0 , h ) (dashed curves). The solid diamonds, solid triangles, and solid squares show the sections of the profile τ p ( 0 , h ) for the height intervals, 500–1935, 1935–3090, and 3090–5000 m, retrieved with the column-integrated lidar ratios 27, 56.2, and 21.7 sr, respectively.

Fig. 8
Fig. 8

Noise-corrupted vertical profile of the particulate backscatter coefficient, β p ( 0 , h ) , measured at the wavelength 355   nm in a clear, cloudless atmosphere.

Fig. 9
Fig. 9

Dotted curve is the nonsmoothed vertical profile of the particulate optical depth, τ p ( 0 , h ) , measured at 355   nm in a clear, cloudless atmosphere. Dashed curves 1 and 2 show the profiles of τ p , l o w ( 0 , h ) and τ p , u p ( 0 , h ) , respectively, and thin solid curve 3 is the base profile, τ p , b ( 0 , h ) . The thick solid curve shows the profile τ p ( 0 , h ) retrieved assuming a stepwise column-integrated ratio.

Fig. 10
Fig. 10

Column-integrated lidar ratios (the thick vertical lines), the profile of S p ( h ) obtained from Eq. (1) (the solid dots), and that obtained with Eq. (14) (the solid curve).

Fig. 11
Fig. 11

Profile of κ p ( h ) retrieved using the new method (the thick solid curve) and that obtained using the conventional numerical differentiation method with a range resolution of 500 m (the dotted curve). In the bottom of the figure, the range of the monotonic change of the ground-based nephelometer data during the lidar measurement is shown.

Equations (15)

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κ p ( h ) = S p ( h ) β p ( h ) .
τ p ( h j , h ) = h j h κ p ( h ) d h = h j h S p ( h ) β p ( h ) d h .
τ p ( h j , h ) = S p , j ( h j , h ) h j h β p ( h ) d h ,
S p , j ( h j , h ) = h j h S p ( h ) β p ( h ) d h h j h β p ( h ) d h .
τ p ( h j , h ) = S p , j h j h β p ( h ) d h .
Δ τ p , j ( h ) = S p , j h i h β p ( h ) d h S p , j ( h j , h ) h i h β p ( h ) d h .
| Δ τ p , j ( h ) | Δ τ p , max ( h )
κ p ( h ) S p , j β p ( h ) .
Δ τ p , max ( h ) = max [ Δ τ p ( h min ) ; Δ τ p ( h min + Δ h d ) ; Δ τ p ( h min + 2 Δ h d ) ; ; Δ τ p ( h ) ] .
τ p ( 0 , h ) = τ p , b ( 0 , h j ) + τ p ( h j , h ) = τ p , b ( 0 , h j ) + [ S p , j h j h β p ( h ) d h ] ,
ξ ( h k , h max ) = h k h max [ τ p ( 0 , h ) τ p , b ( 0 , h ) ] 2 .
δ κ p ( h ) = [ δ β p ( h ) ] 2 + [ δ S p ( h ) ] 2 .
| Δ S p , j ( h ) | = | S p , j S p , j ( h j , h ) | Δ τ p , max ( h ) h j h β p ( h ) d h .
S p ( h ) = S p ( h 1 , h ) + h 1 h β p ( h ) d h β p ( h ) d d h [ S p ( h 1 , h ) ] ,
S p ( h 1 , h ) = τ p , b ( h 1 , h ) h 1 h β p ( h ) d h .

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