Abstract

A sensitivity study with an inversion scheme that permits one to retrieve physical parameters of tropospheric particle size distributions, e.g., effective radius, volume, surface-area, and number concentrations, as well as the mean complex refractive index from backscatter and extinction coefficients at multiple wavelengths is presented. The optical data for the analysis are derived from Mie-scattering calculations for monomodal and bimodal logarithmic-normal distributions in the particle size range between 0.01 and 10 µm. The complex refractive index is taken between 1.33 and 1.8 in the real part and between 0 and 0.1 in the imaginary part. The choice of these parameters takes account of properties of optically active atmospheric particles. The wavelengths were chosen at 355, 400, 532, 710, 800, and 1064 nm for the backscatter and at 355 and 532 nm for the extinction data, which are the available wavelengths of the two lidar systems at the Institute for Tropospheric Research. Cases of erroneous optical data of the order of as much as 20%, an unknown refractive index, which may also be wavelength and size dependent, as well as the a priori unknown modality of the particle size distribution were considered. It is shown that both extinction channels are necessary for determining the above-mentioned parameters within reasonable limits, i.e., effective radius, surface-area, and volume concentrations to an accuracy of ±50%, the real part of the complex refractive index to ±0.1, and the imaginary part to ±50%. The number concentration may have errors larger than 50%. The overall performance of the inversion scheme permits the evaluation of experimental data on a routine basis.

© 1999 Optical Society of America

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1999 (1)

1997 (1)

1996 (1)

M. J. Post, “A graphical technique for retrieving size distribution parameters from multiple measurements: visualization and error analysis,” J. Atmos. Oceanic Technol. 13, 863–873 (1996).
[CrossRef]

1995 (2)

1994 (9)

I. N. Tang, H. R. Munkelwitz, “Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance,” J. Geophys. Res. 99, 18,801–18,808 (1994).
[CrossRef]

P. K. Koutsenogii, R. Jaenicke, “Number concentration and size distribution of atmospheric aerosol in Siberia,” J. Aerosol Sci. 25, 377–383 (1994).
[CrossRef]

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10,341–10,356 (1994).
[CrossRef]

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

B. Stein, M. Del Guasta, J. Kolenda, M. Morandi, P. Rairoux, L. Stefanutti, J. P. Wolf, L. Wöste, “Stratospheric aerosol size distribution from multispectral lidar measurements at Sodankylä during EASOE,” Geophys. Res. Lett. 21, 1311–1314 (1994).
[CrossRef]

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid Southwestern United States: Measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1994).
[CrossRef]

I. S. Kristament, J. B. Liley, M. J. Harvey, “Aerosol variability in the vertical in the Southwest Pacific,” J. Geophys. Res. 98, 7129–7139 (1994).
[CrossRef]

R. F. Pueschel, J. M. Livingston, G. V. Ferry, T. E. DeFelice, “Aerosol abundances and optical characteristics in the Pacific Basin free troposphere,” Atmos. Environ. 28, 951–960 (1994).
[CrossRef]

S. Wen, W. I. Rose, “Retrieval of sizes and total masses of particles in volcanic clouds using AVHRR bands 4 and 5,” J. Geophys. Res. 99, 5421–5431 (1994).
[CrossRef]

1993 (2)

D. S. Covert, J. Heintzenberg, “Size distribution and chemical properties of aerosol at Ny Ålesund, Svalbard,” Atmos. Environ. 27A, 2989–2997 (1993).
[CrossRef]

J. D. Lindberg, R. E. Douglass, D. M. Garvey, “Carbon and the optical properties of atmospheric dust,” Appl. Opt. 32, 6077–6086 (1993).
[CrossRef] [PubMed]

1992 (2)

1991 (1)

D. Nychka, “Choosing a range for the amount of smoothing in nonparametric regression,” J. Am. Stat. Soc. 86, 653–664 (1991).
[CrossRef]

1990 (2)

M. Tanaka, T. Hayasaka, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–345 (1990).

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

1989 (3)

1988 (1)

P. Paatero, T. Raunemaa, R. L. Dod, “Composition characteristics of carbonaceous particle samples, analyzed by EVE deconvolution method,” J. Aerosol Sci. 19, 1223–1226 (1988).
[CrossRef]

1986 (1)

T. Nakajima, T. Takamura, M. Yamano, M. Shiobara, T. Yamauchi, R. Goto, K. Murai, “Consistency of aerosol size distributions inferred from measurements of solar radiation and aerosols,” J. Meteorol. Soc. Jpn. 64, 765–776 (1986).

1984 (1)

E. M. Patterson, C. K. McMahon, “Absorption characteristics of forest fire particulate matter,” Atmos. Environ. 18, 2541–2551 (1984).
[CrossRef]

1983 (1)

1982 (1)

1981 (1)

1980 (1)

C. V. Mathai, A. W. Harrison, “Estimation of atmospheric aerosol refractive index,” Atmos. Environ. 14, 1131–1135 (1980).
[CrossRef]

1979 (2)

G. H. Golub, M. Heath, G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

P. Craven, G. Wahba, “Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation,” Numer. Math. 31, 377–403 (1979).
[CrossRef]

1977 (3)

Ansmann, A.

Arao, K.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki—Part II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Beyerle, G.

G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
[CrossRef]

Böckmann, C.

C. Böckmann, J. Niebsch, “A mollifier method for aerosol size distribution,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Bohren, C. F.

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

Browell, E. V.

Y. Sasano, E. V. Browell, “Light scattering characteristics of various aerosol types derived from multiple wavelength lidar observations,” Appl. Opt. 28, 1670–1679 (1989).
[CrossRef] [PubMed]

W. B. Grant, E. V. Browell, C. F. Butler, G. D. Nowicki, “LITE measurements of biomass burning aerosols and comparisons with correlative airborne lidar measurements of multiple scattering in the planetary boundary layer,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Butler, C. F.

W. B. Grant, E. V. Browell, C. F. Butler, G. D. Nowicki, “LITE measurements of biomass burning aerosols and comparisons with correlative airborne lidar measurements of multiple scattering in the planetary boundary layer,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Carswell, A. I.

D. P. Donovan, A. I. Carswell, “Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements,” Appl. Opt. 36, 9406–9424 (1997).
[CrossRef]

D. P. Donovan, A. I. Carswell, “Retrieval of stratospheric aerosol physical properties using multiwavelength lidar backscatter and extinction measurements,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Castagnoli, F.

J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
[CrossRef]

Covert, D. S.

D. S. Covert, J. Heintzenberg, “Size distribution and chemical properties of aerosol at Ny Ålesund, Svalbard,” Atmos. Environ. 27A, 2989–2997 (1993).
[CrossRef]

Craven, P.

P. Craven, G. Wahba, “Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation,” Numer. Math. 31, 377–403 (1979).
[CrossRef]

d’Almeida, G. A.

G. A. d’Almeida, P. Köppke, E. P. Shettle, Atmospheric Aerosols, Global Climatology, and Radiative Characteristics (Deepak Publishing, Hampton, Va., 1991).

DeFelice, T. E.

R. F. Pueschel, J. M. Livingston, G. V. Ferry, T. E. DeFelice, “Aerosol abundances and optical characteristics in the Pacific Basin free troposphere,” Atmos. Environ. 28, 951–960 (1994).
[CrossRef]

Del Guasta, M.

B. Stein, M. Del Guasta, J. Kolenda, M. Morandi, P. Rairoux, L. Stefanutti, J. P. Wolf, L. Wöste, “Stratospheric aerosol size distribution from multispectral lidar measurements at Sodankylä during EASOE,” Geophys. Res. Lett. 21, 1311–1314 (1994).
[CrossRef]

J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
[CrossRef]

Deshler, T.

Dod, R. L.

P. Paatero, T. Raunemaa, R. L. Dod, “Composition characteristics of carbonaceous particle samples, analyzed by EVE deconvolution method,” J. Aerosol Sci. 19, 1223–1226 (1988).
[CrossRef]

Donovan, D. P.

D. P. Donovan, A. I. Carswell, “Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements,” Appl. Opt. 36, 9406–9424 (1997).
[CrossRef]

D. P. Donovan, A. I. Carswell, “Retrieval of stratospheric aerosol physical properties using multiwavelength lidar backscatter and extinction measurements,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Douglass, R. E.

Fernandez, G.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid Southwestern United States: Measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1994).
[CrossRef]

Ferry, G. V.

R. F. Pueschel, J. M. Livingston, G. V. Ferry, T. E. DeFelice, “Aerosol abundances and optical characteristics in the Pacific Basin free troposphere,” Atmos. Environ. 28, 951–960 (1994).
[CrossRef]

Fraser, R. S.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10,341–10,356 (1994).
[CrossRef]

Fuller, K.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid Southwestern United States: Measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1994).
[CrossRef]

Ganor, E.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10,341–10,356 (1994).
[CrossRef]

Garvey, D. M.

Gillespie, J. B.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, B. H. Stockton, “Complex index of refraction between 300 and 700 nm for Saharan aerosols,” J. Geophys. Res. 82, 3153–3160 (1977).
[CrossRef]

Gitelson, A.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10,341–10,356 (1994).
[CrossRef]

Golub, G. H.

G. H. Golub, M. Heath, G. Wahba, “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).
[CrossRef]

Goto, R.

T. Nakajima, T. Takamura, M. Yamano, M. Shiobara, T. Yamauchi, R. Goto, K. Murai, “Consistency of aerosol size distributions inferred from measurements of solar radiation and aerosols,” J. Meteorol. Soc. Jpn. 64, 765–776 (1986).

Grant, W. B.

W. B. Grant, E. V. Browell, C. F. Butler, G. D. Nowicki, “LITE measurements of biomass burning aerosols and comparisons with correlative airborne lidar measurements of multiple scattering in the planetary boundary layer,” in Advances in Atmospheric Remote Sensing with Lidar, A. Ansmann, R. Neuber, P. Rairoux, U. Wandinger, eds. (Springer-Verlag, Berlin, 1996).

Hansen, A. D. A.

R. G. Pinnick, G. Fernandez, E. Martinez-Andazola, B. D. Hinds, A. D. A. Hansen, K. Fuller, “Aerosol in the arid Southwestern United States: Measurements of mass loading, volatility, size distribution, absorption characteristics, black carbon content, and vertical structure to 7 km above sea level,” J. Geophys. Res. 98, 2651–2666 (1994).
[CrossRef]

Harrison, A. W.

C. V. Mathai, A. W. Harrison, “Estimation of atmospheric aerosol refractive index,” Atmos. Environ. 14, 1131–1135 (1980).
[CrossRef]

Harvey, M. J.

I. S. Kristament, J. B. Liley, M. J. Harvey, “Aerosol variability in the vertical in the Southwest Pacific,” J. Geophys. Res. 98, 7129–7139 (1994).
[CrossRef]

Hayasaka, T.

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

M. Tanaka, T. Hayasaka, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–345 (1990).

Heath, M.

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Schrems, O.

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B. Stein, M. Del Guasta, J. Kolenda, M. Morandi, P. Rairoux, L. Stefanutti, J. P. Wolf, L. Wöste, “Stratospheric aerosol size distribution from multispectral lidar measurements at Sodankylä during EASOE,” Geophys. Res. Lett. 21, 1311–1314 (1994).
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J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
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J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
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T. Nakajima, T. Takamura, M. Yamano, M. Shiobara, T. Yamauchi, R. Goto, K. Murai, “Consistency of aerosol size distributions inferred from measurements of solar radiation and aerosols,” J. Meteorol. Soc. Jpn. 64, 765–776 (1986).

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T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
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M. Tanaka, T. Hayasaka, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–345 (1990).

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T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
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I. N. Tang, H. R. Munkelwitz, “Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance,” J. Geophys. Res. 99, 18,801–18,808 (1994).
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Venturi, V.

J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
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S. Wen, W. I. Rose, “Retrieval of sizes and total masses of particles in volcanic clouds using AVHRR bands 4 and 5,” J. Geophys. Res. 99, 5421–5431 (1994).
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G. Beyerle, R. Neuber, O. Schrems, F. Wittrock, B. Knudsen, “Multiwavelength lidar measurements of stratospheric aerosols above Spitsbergen during winter 1992/93,” Geophys. Res. Lett. 21, 57–60 (1994).
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B. Stein, M. Del Guasta, J. Kolenda, M. Morandi, P. Rairoux, L. Stefanutti, J. P. Wolf, L. Wöste, “Stratospheric aerosol size distribution from multispectral lidar measurements at Sodankylä during EASOE,” Geophys. Res. Lett. 21, 1311–1314 (1994).
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T. Nakajima, T. Takamura, M. Yamano, M. Shiobara, T. Yamauchi, R. Goto, K. Murai, “Consistency of aerosol size distributions inferred from measurements of solar radiation and aerosols,” J. Meteorol. Soc. Jpn. 64, 765–776 (1986).

Yamauchi, T.

T. Nakajima, T. Takamura, M. Yamano, M. Shiobara, T. Yamauchi, R. Goto, K. Murai, “Consistency of aerosol size distributions inferred from measurements of solar radiation and aerosols,” J. Meteorol. Soc. Jpn. 64, 765–776 (1986).

T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
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Zuccagnoli, L.

J. Kolenda, B. Mielke, P. Rairoux, B. Stein, D. Weidauer, J. P. Wolf, L. Wöste, F. Castagnoli, M. Del Guasta, M. Morandi, V. M. Sacco, L. Stefanutti, V. Venturi, L. Zuccagnoli, “Aerosol size distribution measurements using a multispectral lidar system,” in Lidar for Remote Sensing, R. J. Becherer, C. Werner, eds., Proc. SPIE1714, 208–219 (1992).
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Figures (6)

Fig. 1
Fig. 1

Inversion results for the effective radius for different combinations of (β) backscatter and (α) extinction coefficients. The correct values are represented by horizontal lines. The three columns assigned to each line mark the different combinations, i.e., left column, case 1; middle column, case 2; right column, case 3. The crosses show the mean of all accepted solutions; the length of the columns corresponds to the scattering of these solutions (standard deviation). The diamonds show that solution with the smallest deviation between the optical data that were backcalculated from the inverted particle distributions and the input data. The arrows indicate those solutions for which the deviation of the backcalculated optical data to the theoretical ones was larger than 30%.

Fig. 2
Fig. 2

Optical data: (a) backscatter coefficients and (b) extinction coefficients, backcalculated from the inversion results of Table 2 and normalized to the correct values (thick solid lines). For every complex refractive index only that single solution was taken account of that resulted in the smallest deviation to the input data. Solutions with a deviation of less than 20% in each data point are shown only.

Fig. 3
Fig. 3

Same as Fig. 2 but for the case of Table 3.

Fig. 4
Fig. 4

Wavelength-dependent complex refractive index of (a) sea salt and (b) mineral particles44: squares, real part; diamonds, imaginary part. The dashed line at 10-5 in the imaginary part indicates the value below which absorption may be neglected.2

Fig. 5
Fig. 5

Example for the allocation of errors to the optical data. The solid lines and curves connect correct data. If the three backscatter coefficients for the shorter wavelengths as well as the extinction coefficient at 355 nm are imposed with a +5% (-5%) error (indicated by the error bars), the next three backscatter coefficients and the extinction at 532 nm, on the other hand, with -5% (+5%), the dotted and the dashed lines and curves follow.

Fig. 6
Fig. 6

Inversion results for the effective radius for given different error distributions in the optical data for a monomodal distribution. (a) Selection of results for measurement errors of ±5% in the optical data. The solid line corresponds to the correct value of the effective radius of 0.59 µm. The dotted lines present a deviation of ±5%. Each column corresponds to a certain error distribution. Crosses denote the mean value of all (two to 10) solutions taken into account. The lengths of the columns correspond to the standard deviations of these solutions. (b) Same as (a) but for mean errors of ±10% with some data points having errors of 15–20%, others correspondingly less. The dotted lines indicate a deviation of ±10% from the correct value of the effective radius.

Tables (7)

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Table 1 Mean Error of the Sought Parameters as Well as of the Backcalculated Optical Data from All Performed Inversions for Physically Correct Input Data

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Table 2 Inversion Results for Effective Radius of a Monomodal Particle Distribution for Different Refractive Indices

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Table 3 Same as Table 2 but for a Bimodal Distribution

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Table 4 Inversion Results for the Parameters of a Monomodal and a Bimodal Distribution with Unknown Constant Refractive Index

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Table 5 Inversion Results for the Investigated Parameters for an Unknown Wavelength-Dependent Refractive Index, i.e., for a Homogeneous Mixture of Particles in a Monomodal Distribution

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Table 6 Inversion Results for the Investigated Parameters for an Unknown Size-Dependent Refractive Index, i.e., for a Heterogeneous Mixture of Particles

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Table 7 Inversion Results for the Parameters of a Monomodal and a Bimodal Distribution for a Given Measurement Error of ±5% in the Optical Data and Unknown Refractive Index

Equations (4)

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dnr=nt2π1/2 ln σexp-ln r-ln rmod,N22ln σ2d ln r,
reff= nrr3dr nrr2dr,
at=4π  nrr2dr,
vt=4π3  nrr3dr.

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