Abstract

Analysis of signal statistical characteristics is carried out, and estimation errors of the radial wind velocity are calculated by use of numerical simulation of a cw Doppler lidar return, taking into account the atmospheric aerosol microstructure. It has been found that, at small sounded volume, the large particles contribute significantly to the scattered field. As a result the lidar return probability density function distribution can differ significantly from a Gaussian distribution. Neglect of the aerosol microstructure effect results in considerable underestimation of the error of cw Doppler lidar velocity estimates at small sounded volume.

© 2000 Optical Society of America

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  1. V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
    [CrossRef]
  2. V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).
  3. R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
    [CrossRef]
  4. C. M. Sonnenschein, F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10, 1600–1604 (1971).
    [CrossRef] [PubMed]
  5. T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
    [CrossRef]
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media. Vol. 1. Single Scattering and Transport Theory (Academic, New York, 1978), p. 37.
  7. V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), p. 26, in Russian.
  8. Ch. Junge, Chemical Composition and Radioactivity of the Atmosphere (Mir, Moscow, 1965), in Russian.
  9. R. Storm, Wahrscheinlichkeitsrechnung. Mathematiksche Statistic. Statistische Qualitätskontrolle (VEB Fachbuchverlag, Leipzig, 1967).
  10. N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).
  11. I. N. Smalikho, “On measurement of the dissipation rate of turbulent energy dissipation with a cw Doppler lidar,” Atmos. Oceanic Opt. 8, 788–793 (1995).
  12. R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
    [CrossRef] [PubMed]
  13. B. Crosignani, P. Di Porto, M. Bertolotty, Statistical Properties of Scattered Light (Academic, New York, 1975), Chap. 6, p. 186.
  14. D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
    [CrossRef]

1999 (1)

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

1997 (1)

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

1995 (1)

I. N. Smalikho, “On measurement of the dissipation rate of turbulent energy dissipation with a cw Doppler lidar,” Atmos. Oceanic Opt. 8, 788–793 (1995).

1987 (1)

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

1981 (1)

1979 (1)

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

1972 (1)

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

1971 (1)

Banakh, V. A.

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

Bertolotty, M.

B. Crosignani, P. Di Porto, M. Bertolotty, Statistical Properties of Scattered Light (Academic, New York, 1975), Chap. 6, p. 186.

Craver, C. E.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Crosignani, B.

B. Crosignani, P. Di Porto, M. Bertolotty, Statistical Properties of Scattered Light (Academic, New York, 1975), Chap. 6, p. 186.

Di Porto, P.

B. Crosignani, P. Di Porto, M. Bertolotty, Statistical Properties of Scattered Light (Academic, New York, 1975), Chap. 6, p. 186.

Hardesty, R. M.

Horrigan, F. A.

Huffaker, R. M.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media. Vol. 1. Single Scattering and Transport Theory (Academic, New York, 1978), p. 37.

Jones, I. P.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Junge, Ch.

Ch. Junge, Chemical Composition and Radioactivity of the Atmosphere (Mir, Moscow, 1965), in Russian.

Keeler, R. J.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, “Characteristics of coherent lidar returns from calibration targets and aerosols,” Appl. Opt. 20, 3763–3769 (1981).
[CrossRef] [PubMed]

Köpp, F.

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

Krekov, G. M.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), p. 26, in Russian.

Lawrence, T. R.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Lenschow, D. H.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Pinus, N. Z.

N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).

Post, M. J.

Richter, R. A.

Schwiesow, R. L.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Serafin, R. J.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Shmeter, S. M.

N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).

Shur, G. N.

N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).

Smalikho, I. N.

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

I. N. Smalikho, “On measurement of the dissipation rate of turbulent energy dissipation with a cw Doppler lidar,” Atmos. Oceanic Opt. 8, 788–793 (1995).

Sonnenschein, C. M.

Storm, R.

R. Storm, Wahrscheinlichkeitsrechnung. Mathematiksche Statistic. Statistische Qualitätskontrolle (VEB Fachbuchverlag, Leipzig, 1967).

Thomson, J. A.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Vaughan, J. M.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Vinnichenko, N. K.

N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).

Werner, Ch.

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

Wilson, D. J.

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Woodfield, A. A.

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Zrnic, D. S.

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

Zuev, V. E.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), p. 26, in Russian.

Appl. Opt. (2)

Atmos. Oceanic Opt. (2)

V. A. Banakh, Ch. Werner, F. Köpp, I. N. Smalikho, “Fluctuation spectra of wind velocity measured with a Doppler lidar,” Atmos. Oceanic Opt. 10, 202–208 (1997).

I. N. Smalikho, “On measurement of the dissipation rate of turbulent energy dissipation with a cw Doppler lidar,” Atmos. Oceanic Opt. 8, 788–793 (1995).

IEEE Trans. Geosci. Electron. (1)

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

J. Atmos. Oceanic Technol. (2)

V. A. Banakh, I. N. Smalikho, F. Köpp, Ch. Werner, “Measurement of turbulent energy dissipation rate with a cw Doppler lidar in the atmospheric boundary layer,” J. Atmos. Oceanic Technol. 16, 1044–1061 (1999).
[CrossRef]

R. J. Keeler, R. J. Serafin, R. L. Schwiesow, D. H. Lenschow, J. M. Vaughan, A. A. Woodfield, “An airborne laser air motion sensing system. Part I: concept and preliminary experiment,” J. Atmos. Oceanic Technol. 4, 113–127 (1987).
[CrossRef]

Rev. Sci. Instrum. (1)

T. R. Lawrence, D. J. Wilson, C. E. Craver, I. P. Jones, R. M. Huffaker, J. A. Thomson, “A laser velocimeter for remote wind sensing,” Rev. Sci. Instrum. 43, 512–518 (1972).
[CrossRef]

Other (6)

A. Ishimaru, Wave Propagation and Scattering in Random Media. Vol. 1. Single Scattering and Transport Theory (Academic, New York, 1978), p. 37.

V. E. Zuev, G. M. Krekov, Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986), p. 26, in Russian.

Ch. Junge, Chemical Composition and Radioactivity of the Atmosphere (Mir, Moscow, 1965), in Russian.

R. Storm, Wahrscheinlichkeitsrechnung. Mathematiksche Statistic. Statistische Qualitätskontrolle (VEB Fachbuchverlag, Leipzig, 1967).

N. K. Vinnichenko, N. Z. Pinus, S. M. Shmeter, G. N. Shur, Turbulence in the Free Atmosphere (Consultants Bureau, London, 1973).

B. Crosignani, P. Di Porto, M. Bertolotty, Statistical Properties of Scattered Light (Academic, New York, 1975), Chap. 6, p. 186.

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Figures (5)

Fig. 1
Fig. 1

Models of aerosol particle size concentration distribution (points and curves 1 and 2) and dependence of parameter η s on a.

Fig. 2
Fig. 2

Instantaneous distributions of amplitudes A i and fluctuations of radial velocity V r ′ along the sounding path.

Fig. 3
Fig. 3

Time dependences of the lidar return instantaneous power P s (t) and the signal spectra W(V) (solid curves) and [ W2V¯]1/2 (dashed curves).

Fig. 4
Fig. 4

Normalized PDF’s for (a) the amplitude and (b) the power of the signal. Curves 1, 2, and 3 represent R = 10, 50, and 100 m, respectively. The (a) Rayleigh distribution and (b) exponential distribution are denoted by dashed curves.

Fig. 5
Fig. 5

Range dependence of the error of the Doppler velocity estimate. Curve 3 is the result of the numerical simulation of the lidar return distributed according to Gaussian statistics; the dashed curve represents results calculated by Eq. (1); curves 1 and 2 represent the results of numerical simulation obtained with the models in Eqs. (17) and (18) for ρ c (a), respectively.

Tables (1)

Tables Icon

Table 1 Sounded Volume Parameters and Number of Particles in this Volume

Equations (45)

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σe2=18πλt0 σs,
jsnt=jst+jnt,
jst=2ηehνPLPT λ i=1ns AsaiE2rit×expjΨi+j2kVrzit,
Er=PT/πa0gzexp-1+j ka02Rρ22a02gz,
S=Pst=122ηehν2PLPT λ214π σρ0Veff|Ermax|4,
σ=0daσafa
Veff=0dz - d2ρ|Er|4/|Ermax|4
Veff=1/2 SRΔz,
Δz=R2/ka021+R/ka022π2+arctanka02R
aR=λR/2πa0, Δz=λ/2R/a02, Veff=λ316πR4a04.
|Ermax|4=16π21λ4a04R4 PT2=πλPT2Veff.
S=12ηehν2PLPTλβπ,
N=1/2 |jnt|2=2ηe2PLhν B.
SNR=14ηPThνB λβπ.
ρca=ρ0adafa.
fa=-1ρ0dρcada.
ρca=ρ0c11+α1a3+c21+α2a3,
ρca=ρ01+α1a3.
ηsam=0amdaσafa0daσafa=0.1.
P2=n=0Ntn/n!exp-Nt1-1-ρeff/ρ0n=1-exp-Ntρeff/ρ01-exp-NeffUt0/πaR.
j˜snΔtm=j˜sΔtm+ξm/2SNR,
j˜sΔtm=q i=0ns AsaiIzi, ρi-VΔtm×expjΨ0zi, ρi-VΔtm+jΨi+j2kVrziΔtm,
Iz, ρ=a02ab2zexp-ρ2ab2z,
j˜snmΔt=q2πi=nz1nz2a02ab2ΔRi×k=ntnν+nt-1l=1np σ1/2aiklexpjΨ˜ikl×exp-Δxk-nV/2abiΔR2×expj 4πλ VriΔRmΔt+ξm2SNR,
i=nz1nz2i=nvk=1 np
dafa=dξ.
1-ρca/ρ0=ξ.
a=β+β2+4γξ1/22γ1/3,
a=1α1ξ1-ξ1/3,
En=l=1np σ1/2alexpjΨ˜l
En=σ1/2amaxexpjΨ˜.
fna=fai=1nkin-10adakfak.
fna=-nρ0dρcada1-ρca/ρ0n-1.
ρcna=ρcn01-1-ρca/ρ0n.
Q1=n 0dafaσa,Q2=n 0dafa1-ρca/ρ0n-1σa.
SVκ=-+dzBVzexp-2πjκz
SVκ=2σV2LV1+8.42LVκ25/6,
VrΔRi=Vr+Rek=0Nz-1 ξk1ΔRNz SVkΔRNz1/2×exp-2πj kiNz,
JsnkΔf, mT=m=0M-1 j˜snmT+mΔt×exp-2πjkm/M,
WkΔf=1Mm=0M-1 JsnkΔf, mT.
VD=ΔVDk=k1k2 kWs2kΔfk=k1k2 Ws2kΔf,
W2kΔf¯=i=nz1nz2λΔR2πab2ΔRisinc2× πk-2λΔf VrΔRi.
Vr¯=i=nz1nz2λΔR2πab2ΔRi VrΔRi
Ve=VD-V¯r.
i=nz1nz2 Ai expjΨi,

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