Abstract

We developed a mathematical scheme that allows us to improve retrieval products obtained from the inversion of multiwavelength Raman/HSRL lidar data, commonly dubbed “3backscatter+2extinction” (3β+2α) lidar. This scheme works independently of the automated inversion method that is currently being developed in the framework of the Aerosol-Cloud-Ecosystem (ACE) mission and which is successfully applied since 2012 [Atmos. Meas. Tech. 7, 3487 (2014) [CrossRef]  ; “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July  2015, paper PS-C1-14] to data collected with the first airborne multiwavelength 3β+2α high spectral resolution lidar (HSRL) developed at NASA Langley Research Center. The mathematical scheme uses gradient correlation relationships we presented in part 1 of our study [Appl. Opt. 55, 9839 (2016) [CrossRef]  ] in which we investigated lidar data products and particle microphysical parameters from one and the same set of optical lidar profiles. For an accurate assessment of regression coefficients that are used in the correlation relationships we specially designed the proximate analysis method that allows us to search for a first-estimate solution space of particle microphysical parameters on the basis of a look-up table. The scheme works for any shape of particle size distribution. Simulation studies demonstrate a significant stabilization of the various solution spaces of the investigated aerosol microphysical data products if we apply this gradient correlation method in our traditional regularization technique. Surface-area concentration can be estimated with an uncertainty that is not worse than the measurement error of the underlying extinction coefficients. The retrieval uncertainty of the effective radius is as large as ±0.07  μm for fine mode particles and approximately 100% for particle size distributions composed of fine (submicron) and coarse (supermicron) mode particles. The volume concentration uncertainty is defined by the sum of the uncertainty of surface-area concentration and the uncertainty of the effective radius. The uncertainty of number concentration is better than 100% for any radius domain between 0.03 and 10 μm. For monomodal PSDs, the uncertainties of the real and imaginary parts of the CRI can be restricted to ±0.1 and ±0.01 on the domains [1.3; 1.8] and [0; 0.1], respectively.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

5 December 2016: Corrections were made to Eq. (7) and to the Acknowledgment on 5 December 2016.

21 March 2017: A correction was made to the Funding section on 21 March 2017.


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References

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  1. D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
    [Crossref]
  2. P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.
  3. A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).
  4. C. F. Bohren and D. R. Huffman, eds., Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  5. D. Müller, U. Wandinger, and A. Ansmann, “Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2357 (1999).
    [Crossref]
  6. I. Veselovskii, A. Kolgotin, V. Griaznov, D. Müller, U. Wandinger, and D. Whiteman, “Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding,” Appl. Opt. 41, 3685–3699 (2002).
    [Crossref]
  7. C. Böckmann, I. Miranova, D. Müller, L. Scheidenbach, and R. Nessler, “Microphysical aerosol parameters from multiwavelength lidar,” J. Opt. Soc. Am. A 22, 518–528 (2005).
    [Crossref]
  8. A. Kolgotin and D. Müller, “Theory of inversion with two-dimensional regularization: profiles of microphysical particle properties derived from multiwavelength lidar measurements,” Appl. Opt. 47, 4472–4490 (2008).
    [Crossref]
  9. D. Müller, A. Kolgotin, I. Mattis, A. Petzold, and A. Stohl, “Vertical profiles of microphysical particle properties derived from inversion with two-dimensional regularization of multiwavelength Raman lidar data: experiment,” Appl. Opt. 50, 2069–2079 (2011).
    [Crossref]

2014 (1)

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

2011 (1)

2008 (1)

2005 (1)

2002 (1)

1999 (1)

Anderson, B.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Ansmann, A.

Berg, L. K.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Beyersdorf, A.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Böckmann, C.

Burton, S.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Burton, S. P.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Chemyakin, E.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).

Cleckner, C. S.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Cook, A. L.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Ferrare, R.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Ferrare, R. A.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Griaznov, V.

Hair, J. W.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Hare, R. W.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Harper, D. B.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Hostetler, C.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Hostetler, C. A.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Kolgotin, A.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

D. Müller, A. Kolgotin, I. Mattis, A. Petzold, and A. Stohl, “Vertical profiles of microphysical particle properties derived from inversion with two-dimensional regularization of multiwavelength Raman lidar data: experiment,” Appl. Opt. 50, 2069–2079 (2011).
[Crossref]

A. Kolgotin and D. Müller, “Theory of inversion with two-dimensional regularization: profiles of microphysical particle properties derived from multiwavelength lidar measurements,” Appl. Opt. 47, 4472–4490 (2008).
[Crossref]

I. Veselovskii, A. Kolgotin, V. Griaznov, D. Müller, U. Wandinger, and D. Whiteman, “Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding,” Appl. Opt. 41, 3685–3699 (2002).
[Crossref]

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).

Mattis, I.

Miranova, I.

Müller, D.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

D. Müller, A. Kolgotin, I. Mattis, A. Petzold, and A. Stohl, “Vertical profiles of microphysical particle properties derived from inversion with two-dimensional regularization of multiwavelength Raman lidar data: experiment,” Appl. Opt. 50, 2069–2079 (2011).
[Crossref]

A. Kolgotin and D. Müller, “Theory of inversion with two-dimensional regularization: profiles of microphysical particle properties derived from multiwavelength lidar measurements,” Appl. Opt. 47, 4472–4490 (2008).
[Crossref]

C. Böckmann, I. Miranova, D. Müller, L. Scheidenbach, and R. Nessler, “Microphysical aerosol parameters from multiwavelength lidar,” J. Opt. Soc. Am. A 22, 518–528 (2005).
[Crossref]

I. Veselovskii, A. Kolgotin, V. Griaznov, D. Müller, U. Wandinger, and D. Whiteman, “Inversion with regularization for the retrieval of tropospheric aerosol parameters from multiwavelength lidar sounding,” Appl. Opt. 41, 3685–3699 (2002).
[Crossref]

D. Müller, U. Wandinger, and A. Ansmann, “Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2357 (1999).
[Crossref]

A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Nessler, R.

Obland, M. D.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Petzold, A.

Rogers, R. R.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Romanov, A.

A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).

Sawamura, P.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Scheidenbach, L.

Schmid, B.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Stohl, A.

Tomlinson, J.

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

Veselovskii, I.

Wandinger, U.

Whiteman, D.

Ziemba, L.

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

Appl. Opt. (4)

Atmos. Meas. Tech. (1)

D. Müller, C. A. Hostetler, R. A. Ferrare, S. P. Burton, E. Chemyakin, A. Kolgotin, J. W. Hair, A. L. Cook, D. B. Harper, R. R. Rogers, R. W. Hare, C. S. Cleckner, M. D. Obland, J. Tomlinson, L. K. Berg, and B. Schmid, “Airborne multiwavelength high spectral resolution lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US,” Atmos. Meas. Tech. 7, 3487–3496 (2014).
[Crossref]

J. Opt. Soc. Am. A (1)

Other (3)

P. Sawamura, D. Müller, S. Burton, E. Chemyakin, C. Hostetler, R. Ferrare, A. Kolgotin, L. Ziemba, A. Beyersdorf, and B. Anderson, “Comparison of aerosol optical and microphysical retrievals from HSRL-2 and in-situ measurements during DISCOVER-AQ 2013 (California and Texas),” in International Laser Radar Conference, July 2015, paper PS-C1-14.

A. Kolgotin, D. Müller, E. Chemyakin, and A. Romanov, “Improved identification of the solution space of aerosol microphysical properties derived from the inversion of profiles of lidar optical data, part 1: theory,” Appl. Opt.55, 9839–9849 (2016).

C. F. Bohren and D. R. Huffman, eds., Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (4)

Fig. 1.
Fig. 1. Numerical example: vertical profile of type 1. Shown are the retrieval results for the case of a 3 β + 2 α data set, i.e., (a) true input data (solid line) and distorted data (closed symbols) of the backscatter and extinction coefficients. Also shown are the respective BAE for the wavelength pair 532/1064 nm and the EAE for the wavelength pair 355/532 nm. (b)–(e): true (thick line) and retrieved (line + symbol) results for PMP, CRI, and PSD. The retrieval results were obtained when GCM was not used (triangles), when GCM was used with the true RCs (squares), and when GCM was used with incorrect RCs (dashed line). We assumed that the true PSD was either monomodal (MMS) or bimodal (BMS) and that a s = 1.6 . The asterisks describe the PA of the fine mode parameters. Stars denote the retrieval results of the CRI of the fine mode particles that follow from the combination of PA with the results of an effective radius that is obtained with GCM.
Fig. 2.
Fig. 2. Numerical example: vertical profile of type 1. The statistics are shown for the true (circles) and the retrieved values obtained for the case that we do not use GCM (triangles), the case that we use GCM with the true RCs (squares), and the case that we use GCM with incorrect RCs (dashed lines). We assumed that the PSD is either monomodal (MMS) or bimodal (BMS), and that a s = 1.6 . The solid lines describe the correlation trends according to the equation y = a x + b and R 2 . The regression equations are given in the legends.
Fig. 3.
Fig. 3. Numerical example: vertical profile of type 2. The meaning of the lines, symbols, and colors is the same as in Fig. 1.
Fig. 4.
Fig. 4. Numerical example: vertical profile of type 2. The meaning of the lines, symbols, and colors is the same as in Fig. 2.

Tables (5)

Tables Icon

Table 1. Example of PA of Particle Microphysical Parameters of the Fine Mode Fraction of a PSD

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Table 2. Particle Fine Mode Fractions Found with PA for the Example of Height Bin l = 6 in Table 1

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Table 3. Vertical Profile of Type 1: Regression Coefficients and Thresholds that Can Be Used as Constraints in the Next Version of the Postprocessing of the Solution Space Provided by the Automated, Unsupervised Inversion Algorithm

Tables Icon

Table 4. Variations of the RCs of the SOD Bank

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Table 5. Vertical Profile Type 2: Regression Coefficients and Thresholds that Can Be Used as Constraints in the Future Postprocessing of the Solution Space Provided by the Automated, Unsupervised Inversion Algorithm

Equations (44)

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

p = a p α ( 355 ) + b p ,
p = s , v / r eff , n ( r mean 2 + σ 2 )    in    μm 2    cm 3 = Mm 1 .
a s [ 1.3 ; 1.9 ] , a v [ 0.4 ; 0.6 ] , a n [ 0.11 ; 0.15 ] ,
b p = 0 , p = s , v / r eff , n ( r mean 2 + σ 2 ) ,
r eff = a r å α + b r ,
a r [ 10 ; 0.038 ] , b r [ 0.18 ; 0.5 ]    in    μm .
p = a p r eff + b p ,
p = r mean , σ in    μm ,
a m [ 0.17 ; 0.84 ] , a σ [ 0.21 ; 0.31 ] ,
b p 0 , p = r mean , σ .
ρ LUT = 1 5 p | p LUT p experiment | p LUT , p = å α , å β ( 355 ) , β ( 532 ) , α ( 355 ) / β ( 355 ) , α ( 532 ) / β ( 532 ) , r eff .
r min ( l ) r max ( l ) K g ( λ , m ( l ) , r ) f ( l ) ( r ) d r = g ( l ) ( λ ) , l = 1 , , N L ; g = α , β .
| p i ( l ) p av | < δ p .
r eff ( l ) * = a r å α ( l ) + b r .
| r eff , i ( l ) r eff ( l ) * | < δ r eff .
| p i ( l ) p ( l ) * | < δ p and p = s , v / r eff , n ( r mean 2 + σ 2 ) .
r eff 0.08 å α + 0.26 ,
s 1.6 α ( 355 ) ,
v 1.6 α ( 355 ) × ( 0.08 å + 0.26 ) / 3 .
n 1.6 α ( 355 ) 4 π ( 0.08 å + 0.26 ) 2 .
g ( λ ) = g f ( λ ) + g c ( λ ) = φ g g ( λ ) + ( 1 φ g ) g ( λ ) , g = α , β ,
g c ( λ ) g f ( λ ) = g ( λ ) g f ( λ ) 1 = 1 φ g 1 g = a , b .
α f ( 532 ) + α c ( 532 ) α f ( 355 ) + α c ( 355 ) = α ( 532 ) α ( 355 ) ,
α f ( 532 ) = α ( 532 ) α ( 355 ) [ α f ( 355 ) + α c ( 355 ) ] α c ( 532 ) .
α f ( 532 ) α f ( 355 ) = 1 φ α ( 355 ) [ α ( 532 ) α ( 355 ) + d c ( φ α ( 355 ) 1 ) ] ,
d c = α c ( 532 ) / α c ( 355 ) .
å a , f = ln { 1 φ α ( 355 ) [ α ( 532 ) α ( 355 ) + d c ( φ α ( 355 ) 1 ) ] } ln 355 532 å a .
r eff , f 0.08 å α , f + 0.26 ,
s f 1.6 α f ( 355 ) = 1.6 φ α ( 355 ) α ( 355 ) ,
v f s f r eff , f / 3 .
n f , max = 1 4 π s f r mean , f 2 + σ f 2 1 2 π s f r eff , f 2 .
n f , min = 1 4 π s f r mean , f 2 + σ f 2 1 4 π s f r eff , f 2 .
φ α ( 532 ) = 1 ( 1 φ α ( 355 ) ) d c α ( 355 ) α ( 532 ) .
φ β ( 355 ) = φ α ( 355 ) α ( 355 ) β ( 355 ) β f ( 355 ) α f ( 355 ) ,
φ β ( 532 ) = φ α ( 532 ) α ( 532 ) β ( 532 ) β f ( 532 ) α f ( 532 ) .
å β ( 355 ) , β ( 532 ) , f = å β ( 355 ) , β ( 532 ) + ln φ β ( 532 ) φ β ( 355 ) ln 1 355 532 .
φ β ( 1064 ) = φ β ( 532 ) [ 532 1064 ] å β ( 532 ) , β ( 1064 ) , f å β ( 532 ) , β ( 1064 ) .
0 φ α ( 532 ) < φ α ( 355 ) 1 , 0 φ β ( 064 ) < φ β ( 532 ) < φ β ( 355 ) 1 , d c [ 1 ; 1.07 ] .
ρ LUT , c = 1 5 p | p LUT p c | p LUT , p = å α , å β ( 355 ) , β ( 532 ) , å β ( 532 ) , β ( 1064 ) , α ( 355 ) / β ( 355 ) , α ( 532 ) / β ( 532 ) ,
φ α ( 355 ) ( 6 ) = 0.52 , φ α ( 532 ) ( 6 ) = 0.37 , φ β ( 355 ) ( 6 ) = 0.43 , φ β ( 532 ) ( 6 ) = 0.24 , φ β ( 1064 ) ( 6 ) = 0.08 .
φ α ( 355 ) ( 4 ) = 0.88 , φ α ( 532 ) ( 4 ) = 0.79 , φ β ( 355 ) ( 4 ) = 0.80 , φ β ( 532 ) ( 4 ) = 0.60 , φ β ( 1064 ) ( 4 ) = 0.31.
r eff , f ( 1 ) 0.193 × 0.6 + 0.37 = 0.25 ± 0.08    μm ( 0.24    μm ) s f ( 1 ) 1.6 × 1 × 0.07 = 0.11 ± 20 %    μm 2 cm 3 ( 0.136    μm 2 cm 3 ) v f ( 1 ) 0.11 × 0.25 / 3 = 0.009 ± 20 %    μm 2 cm 3 ( 0.011    μm 3 cm 3 ) n f , min ( 1 ) 0.11 / ( 4 × 3.14 × 0.25 2 ) = 0.14    cm 3 ( 1    cm 3 ) n f , max ( 1 ) 0.11 / [ ( 2 × 3.14 × 0.25 2 ) ] = 0.28    cm 3 ( 1    cm 3 )
ρ LUT = 1 5 p | p LUT p experiment | p LUT , p = å α , å β ( 355 ) , β ( 532 ) , å β ( 532 ) , β ( 1064 ) , α ( 355 ) / β ( 355 ) , α ( 532 ) / β ( 532 ) ,
φ α ( 355 ) ( 2 ) = 0.5 , φ α ( 532 ) ( 2 ) = 0.5 , φ β ( 355 ) ( 2 ) = 0.3 , φ β ( 532 ) ( 2 ) = 0.2 , φ β ( 1064 ) ( 2 ) = 0.06 , φ α ( 355 ) ( 6 ) = 0.5 , φ α ( 532 ) ( 6 ) = 0.5 , φ β ( 355 ) ( 6 ) = 0.6 , φ β ( 532 ) ( 6 ) = 0.5 , φ β ( 1064 ) ( 6 ) = 0.4.

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