Abstract

We present a modified technique for processing multiangle lidar data that is applicable for relatively clear atmospheres, where the utilization of the conventional Kano–Hamilton method meets significant issues. Our retrieval algorithm allows computing the two-way transmission and the corresponding extinction-coefficient profile in any slope direction searched during scanning. These parameters are obtained from the backscatter term of the Kano–Hamilton solution and the corresponding square-range-corrected signal; the second component of the solution, related with the vertical optical depth, is completely excluded from consideration. The inversion technique was used to process experimental data obtained with the Missoula Fire Sciences Laboratory lidar. Simulated and real experimental data are presented that illustrate the essentials of the data-processing technique and possible variants of the extinction-coefficient profile retrieval.

© 2011 Optical Society of America

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  1. M. Kano, “On the determination of backscattering and extinction coefficient of the atmosphere by using a laser radar,” Papers Meteorol. Geophys. 19, 121–129 (1968).
  2. P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
    [CrossRef]
  3. V. A. Kovalev and W. E. Eichinger, Elastic Lidar. Theory, Practice, and Analysis Methods (Wiley-Interscience, 2004), pp. 295–304.
    [CrossRef]
  4. D. N. Whiteman, “Application of statistical methods to the determination of slope in lidar data,” Appl. Opt. 38, 3360–3369(1999).
    [CrossRef]
  5. 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]
  6. F. Rocadenbosch, A. Comeron, and D. Pineda, “Assessment of lidar inversion errors for homogeneous atmospheres,” Appl. Opt. 37, 2199–2206 (1998).
    [CrossRef]
  7. L. Fiorani, B. Calpini, L. Jaquet, H. Van den Bergh, and E. Durieux, “Correction scheme for experimental biases in differential absorption lidar tropospheric ozone measurements based on the analysis of shot per shot data samples,” Appl. Opt. 36, 6857–6863 (1997).
    [CrossRef]
  8. 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. 24, 2014–2028 (2007).
    [CrossRef]
  9. G. J. Kunz and G. de Leeuw, “Inversion of lidar signals with the slope method,” Appl. Opt. 32, 3249–3256 (1993).
    [CrossRef] [PubMed]
  10. V. Shcherbakov, “Regularized algorithm for Raman lidar data processing,” Appl. Opt. 46, 4879–4889 (2007).
    [CrossRef] [PubMed]
  11. B. Cadet, V. Giraud, M. Haeffelin, P. Keckhut, A. Rechou, and S. Baldy, “Improved retrievals of the optical properties of cirrus clouds by a combination of lidar methods,” Appl. Opt. 44, 1726–1734 (2005).
    [CrossRef] [PubMed]
  12. V. Kovalev, “Determination of slope in lidar data using a duplicate of the inverted function,” Appl. Opt. 45, 8781–8789(2006).
    [CrossRef] [PubMed]
  13. V. A. Kovalev, W. M. Hao, and C. Wold, “Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles,” Appl. Opt. 46, 8627–8634 (2007).
    [CrossRef] [PubMed]
  14. V. 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,” Proc. SPIE 6750, 67501B (2007).
    [CrossRef]
  15. G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bösenberg, V. Matthias, V. Amiridis, F. De Tomasi, M. Frioud, M. Iarioti, L. Komguem, A. Papayannis, F. Rocadenbosch, and X. Wang, “Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio,” Appl. Opt. 43, 5370–5385 (2004).
    [CrossRef] [PubMed]
  16. S. Godin, A. Carswell, D. Donovan, H. Claude, W. Steinbrecht, I. McDermid, T. McGee, M. Gross, H. Nakane, D. Swart, H. Bergwerff, O. Uchino, P. Gathen, and R. Neuber, “Ozone differential absorption lidar algorithm intercomparison,” Appl. Opt. 38, 6225–6236 (1999).
    [CrossRef]

2007

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. 24, 2014–2028 (2007).
[CrossRef]

V. Shcherbakov, “Regularized algorithm for Raman lidar data processing,” Appl. Opt. 46, 4879–4889 (2007).
[CrossRef] [PubMed]

V. A. Kovalev, W. M. Hao, and C. Wold, “Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles,” Appl. Opt. 46, 8627–8634 (2007).
[CrossRef] [PubMed]

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

2006

2005

2004

2002

1999

1998

1997

1993

1969

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

1968

M. Kano, “On the determination of backscattering and extinction coefficient of the atmosphere by using a laser radar,” Papers Meteorol. Geophys. 19, 121–129 (1968).

Adam, M.

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. 24, 2014–2028 (2007).
[CrossRef]

Amiridis, V.

Amodeo, A.

Ansmann, A.

Baldy, S.

Bergwerff, H.

Bösenberg, J.

Cadet, B.

Calpini, B.

Carswell, A.

Claude, H.

Comeron, A.

de Leeuw, G.

De Tomasi, F.

Donovan, D.

Durieux, E.

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar. Theory, Practice, and Analysis Methods (Wiley-Interscience, 2004), pp. 295–304.
[CrossRef]

Fiorani, L.

Frioud, M.

Gathen, P.

Giraud, V.

Godin, S.

Gross, M.

Haeffelin, M.

Hamilton, P. M.

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

Hao, W. M.

V. A. Kovalev, W. M. Hao, and C. Wold, “Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles,” Appl. Opt. 46, 8627–8634 (2007).
[CrossRef] [PubMed]

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. 24, 2014–2028 (2007).
[CrossRef]

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

Iarioti, M.

Jaquet, L.

Kano, M.

M. Kano, “On the determination of backscattering and extinction coefficient of the atmosphere by using a laser radar,” Papers Meteorol. Geophys. 19, 121–129 (1968).

Kaul, B. V.

Keckhut, P.

Komguem, L.

Kovalev, V.

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

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. 24, 2014–2028 (2007).
[CrossRef]

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

Kovalev, V. A.

Kunz, G. J.

Matthias, V.

McDermid, I.

McGee, T.

Nakane, H.

Neuber, R.

Newton, J.

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. 24, 2014–2028 (2007).
[CrossRef]

Nordgren, B.

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

Pahlow, M.

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. 24, 2014–2028 (2007).
[CrossRef]

Pandolfi, M.

Papayannis, A.

Pappalardo, G.

Parlange, M. B.

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. 24, 2014–2028 (2007).
[CrossRef]

Pineda, D.

Rechou, A.

Rocadenbosch, F.

Shcherbakov, V.

Shelefontuk, D. I.

Steinbrecht, W.

Swart, D.

Uchino, O.

Van den Bergh, H.

Volkov, S. N.

Wandinger, U.

Wang, X.

Whiteman, D. N.

Wold, C.

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. 24, 2014–2028 (2007).
[CrossRef]

V. A. Kovalev, W. M. Hao, and C. Wold, “Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles,” Appl. Opt. 46, 8627–8634 (2007).
[CrossRef] [PubMed]

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

Appl. Opt.

D. N. Whiteman, “Application of statistical methods to the determination of slope in lidar data,” Appl. Opt. 38, 3360–3369(1999).
[CrossRef]

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]

F. Rocadenbosch, A. Comeron, and D. Pineda, “Assessment of lidar inversion errors for homogeneous atmospheres,” Appl. Opt. 37, 2199–2206 (1998).
[CrossRef]

L. Fiorani, B. Calpini, L. Jaquet, H. Van den Bergh, and E. Durieux, “Correction scheme for experimental biases in differential absorption lidar tropospheric ozone measurements based on the analysis of shot per shot data samples,” Appl. Opt. 36, 6857–6863 (1997).
[CrossRef]

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

V. Shcherbakov, “Regularized algorithm for Raman lidar data processing,” Appl. Opt. 46, 4879–4889 (2007).
[CrossRef] [PubMed]

B. Cadet, V. Giraud, M. Haeffelin, P. Keckhut, A. Rechou, and S. Baldy, “Improved retrievals of the optical properties of cirrus clouds by a combination of lidar methods,” Appl. Opt. 44, 1726–1734 (2005).
[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]

V. A. Kovalev, W. M. Hao, and C. Wold, “Determination of the particulate extinction-coefficient profile and the column-integrated lidar ratios using the backscatter-coefficient and optical-depth profiles,” Appl. Opt. 46, 8627–8634 (2007).
[CrossRef] [PubMed]

G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bösenberg, V. Matthias, V. Amiridis, F. De Tomasi, M. Frioud, M. Iarioti, L. Komguem, A. Papayannis, F. Rocadenbosch, and X. Wang, “Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio,” Appl. Opt. 43, 5370–5385 (2004).
[CrossRef] [PubMed]

S. Godin, A. Carswell, D. Donovan, H. Claude, W. Steinbrecht, I. McDermid, T. McGee, M. Gross, H. Nakane, D. Swart, H. Bergwerff, O. Uchino, P. Gathen, and R. Neuber, “Ozone differential absorption lidar algorithm intercomparison,” Appl. Opt. 38, 6225–6236 (1999).
[CrossRef]

Atmos. Environ.

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

J. Atmos. Ocean. Technol.

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. 24, 2014–2028 (2007).
[CrossRef]

Papers Meteorol. Geophys.

M. Kano, “On the determination of backscattering and extinction coefficient of the atmosphere by using a laser radar,” Papers Meteorol. Geophys. 19, 121–129 (1968).

Proc. SPIE

V. 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,” Proc. SPIE 6750, 67501B (2007).
[CrossRef]

Other

V. A. Kovalev and W. E. Eichinger, Elastic Lidar. Theory, Practice, and Analysis Methods (Wiley-Interscience, 2004), pp. 295–304.
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

True linear fit y ( h ) (solid line), and two shifted lines, y ( h ) and y ( h ) , obtained due to the violation of the requirement of a horizontally stratified atmosphere in Eq. (1). The dashed line, y ( h ) , is obtained when β π , 30 ( h ) = 0.7 β π , 90 ( h ) , and the dotted line, y ( h ) , is obtained when β π , 30 ( h ) = 1.3 β π , 90 ( h ) . The intersection points at x = 0 are obtained by extrapolating the linear fits determined for the points x = 1 and x = 2 .

Fig. 2
Fig. 2

Dependence of the relative errors in the total and particulate optical depths (dotted and dashed curves, respectively) and the corresponding errors in [ C β π ( h ) ] (thick solid curves) versus total vertical optical depth for the cases shown in Fig. 1. The solid horizontal lines with filled circles represent the errors in the profiles [ C β π ( h ) ] , caused by the violation of the requirement of a stratified atmosphere in Eq. (2); here x = 1 and Δ τ 90 ( 0 , h ) = ± 0.05 .

Fig. 3
Fig. 3

Schematic of the multiangle measurement (right panel) and the vertical profile of [ C β π ( h ) ] extracted from the whole set of multiangle data (left panel).

Fig. 4
Fig. 4

Model profile of the vertical two-way particulate transmittance T p , 90 2 ( h 90 , min , h ) (solid curve) and that extracted from the lidar multiangle data (dashed curve).

Fig. 5
Fig. 5

Profiles of κ p * ( h ) obtained by the numerical differentiation of the profiles T p , i 2 ( h i , min , h ) retrieved from the lidar signals measured at φ i = 90 ° (thick solid curve), φ i = 30 ° (gray curve with filled triangles), and φ i = 45 ° (open circles). The thin solid curve is the model profile of the synthetic atmosphere used for the simulations.

Fig. 6
Fig. 6

Schematic of the eight overlapping intervals selected for the total measurement range from r min = 500 m to r max = 7000 m . To clarify the symbols used in the text, the beginning and the end of the fifth interval, the ranges r 5 and r 5 , are marked.

Fig. 7
Fig. 7

Profiles of the particulate extinction coefficient κ p , 90 ( h ) extracted from T p , 90 2 ( h 90 , min , h ) presented in Fig. 4. The thick black curve shows κ p ( h ) extracted using the constant C max = 1.08 C , whereas the gray dots show the extinction coefficient retrieved with the constant C that is 2 times less than the model value. The thin solid curve is the model profile of the extinction coefficient, the same as in Fig. 5.

Fig. 8
Fig. 8

Vertical profiles of the particulate extinction coefficient retrieved from the signal measured at φ i = 45 ° . The thin solid curve is the model profile, the same as that in Fig. 7, and the thick solid curve is the profile derived with the new technique. The dashed curve shows the profile of κ p * ( h ) retrieved using the derivative with the slope range resolution of 510 m .

Fig. 9
Fig. 9

Transmittance profiles T tot , 15 2 ( 0 , h ) (solid curve) and T tot , 68 2 ( 0 , h ) (dotted curve) measured from the azimuthally averaged lidar signals recorded in the elevation angles 15 ° and 68 ° .

Fig. 10
Fig. 10

Particulate extinction-coefficient profiles retrieved from T tot , 15 2 ( 0 , h ) calculated for the elevation angle φ i = 15 ° . The thick gray curve shows the average profile of stepwise extinction coefficient κ p ( h ) , and the thick black curve is the same profile obtained with the weighted average. The dashed–dotted curve is the profile κ p * ( h ) obtained through numerical differentiation with the slope resolution of 500 m .

Fig. 11
Fig. 11

Particulate extinction-coefficient profiles retrieved from T tot , 68 2 ( 0 , h ) . The thick gray curve shows the average profile of stepwise extinction coefficient κ p ( h ) , and the thick black curve is the profile obtained with the weighted average.

Fig. 12
Fig. 12

Slope profiles of vertical transmittance T tot , i , 90 2 ( 0 , h ) obtained from azimuthally averaged signals. The black solid curve on the left is the profile retrieved for the slope direction of φ i = 80 ° .

Fig. 13
Fig. 13

Two-way particulate transmittance profiles extracted from the set of profiles shown in Fig. 12. The gray curve shows the average particulate profile T p , aver , 90 2 ( 0 , h ) , and the black curve shows the minimal profile T p , min , 90 2 ( 0 , h ) . Both profiles are obtained after excluding T tot , 80 2 ( 0 , h ) .

Fig. 14
Fig. 14

Particulate extinction-coefficient profiles retrieved from T part , min , 90 2 ( 0 , h ) . The thick gray curve shows the average profile of stepwise extinction coefficient κ p ( h ) , and the thick black curve is the same profile obtained using the weighted average. The dashed curve is the profile obtained through the numerical differentiation of the profile T part , min , 90 2 ( r min , r i ) using the resolution range of 500 m .

Equations (21)

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β π ( h ) = const.
τ i ( 0 , h ) = τ 90 ( 0 , h ) sin φ i .
y i ( h ) = ln [ P i ( h ) ( h / sin φ i ) 2 ] .
y i ( h ) = A ( h ) 2 τ 90 ( 0 , h ) sin φ i ,
A ( h ) = ln [ C β π ( h ) ] ,
ln [ β π ( h ) β π ( h ) ] = 2 x 0 [ τ 90 ( 0 , h ) τ 90 ( 0 , h ) ] .
δ = exp [ 2 x 0 Δ τ 90 ( 0 , h ) ] 1.
P i ( r i ) r i 2 = C β π ( r i ) T tot , i 2 ( 0 , r i ) ,
T tot , i 2 ( 0 , r i ) = P i ( r i ) r i 2 [ C β π ( h i ) ] ,
κ p * ( r i ) = 0.5 d d r ln [ T p , i 2 ( 0 , r i ) ] .
T p , i 2 ( r , r i ) = T tot , i 2 ( 0 , r i ) T m , i 2 ( 0 , r ) T tot , i 2 ( 0 , r ) T m , i 2 ( 0 , r i ) .
κ p ( h ) = S p , i ( h , h ) β π , p ( h ) ,
T p , i 2 ( r , r i ) = exp [ 2 r r i κ p ( x ) d x ] .
T p , i 2 ( r , r i ) = A 1 B 1 r i ,
T p , i 2 ( r , r i ) = A 2 B 2 r i .
Λ = ( B 1 B 2 ) 2 .
C = [ C β π ( h ref ) ] β π , m ( h ref ) .
C min γ ( h ) ,
γ ( h ) = [ C β π ( h ) ] β π , m ( h ) .
β π , p ( h ) = [ C β π ( h ) ] C β π , m ( h ) .
w = { 1 n ( r m , r n ) r m r n [ T p , i 2 ( r m , r i ) T p , i 2 ( r m , r i ) ] 2 } 1 ,

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