Abstract

Clear-air turbulence could be detected at long range using a UV lidar. Because the vertical speed cannot be retrieved from Doppler shift analysis at long range, the turbulence detection is based on the measurement of molecular density fluctuation associated with the turbulent wind. After an optimization of the characteristics of the candidate UV lidar, we present an evaluation of the detection range and of the false alarm rate and missed alarm rate depending on the altitude and vertical velocity root mean square. This study shows that 96% of turbulence with vertical velocity leading to dislodging of unsecured objects in the airplane can be detected at 15km using a 2W laser at 355nm with a false alarm rate of 0.18 per flight hour.

© 2009 Optical Society of America

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References

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  1. S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.
  2. N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.
  3. U. S. Military specification MIL-F-8785C (1980), paragraph 3.7 Atmospheric disturbances.
  4. S. Gage, “Creating a unified graphical wind turbulence model from multiple specifications,” in American Institute of Aeronautics and Astronautics (AIAA) 2003 Modeling and Simulation Technologies Conference and Exhibit (AIAA, 2003), paper 5529.
  5. C. W. Campbell, “Monte Carlo turbulence simulation using rational approximation to Von Karman spectra,” AIAA J. 24, 62-66 (1986).
    [CrossRef]
  6. D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
    [CrossRef]
  7. C. Cot, F. Dalaudier, and A. Hauchecorne, Service d'Aéronomie du CNRS, BP 3, 91371 Verrières Le Buisson Cedex (personal communication, 2001).
  8. A. Behrendt, “Temperature measurements with lidar,” in Lidar, Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 281-286.
  9. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211-220 (1981).
    [CrossRef] [PubMed]
  10. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638-1643 (1985).
    [CrossRef] [PubMed]
  11. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652-653 (1984).
    [CrossRef] [PubMed]
  12. G. J. Kunz and G. de Leeuw, “Inversion of lidar signals with the slope method,” Appl. Opt. 32, 3249-3256 (1993).
    [CrossRef] [PubMed]
  13. F. Rocadenbosch, C. Soriano, A. Comerón, and J.-M. Baldasano, “Lidar inversion of atmospheric backscatter and extinction-to-backscatter ratios by use of a Kalman filter,” Appl. Opt. 38, 3175-3189 (1999).
    [CrossRef]
  14. A. V. Jelalian, “Detection probabilities and false alarm rates,” in Laser Radar Systems (Artech House, 1992), pp. 77-119.

2007 (1)

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

1999 (1)

1993 (1)

1986 (1)

C. W. Campbell, “Monte Carlo turbulence simulation using rational approximation to Von Karman spectra,” AIAA J. 24, 62-66 (1986).
[CrossRef]

1985 (1)

1984 (1)

1981 (1)

Baldasano, J.-M.

Behrendt, A.

A. Behrendt, “Temperature measurements with lidar,” in Lidar, Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 281-286.

Campbell, C. W.

C. W. Campbell, “Monte Carlo turbulence simulation using rational approximation to Von Karman spectra,” AIAA J. 24, 62-66 (1986).
[CrossRef]

Comerón, A.

Cot, C.

C. Cot, F. Dalaudier, and A. Hauchecorne, Service d'Aéronomie du CNRS, BP 3, 91371 Verrières Le Buisson Cedex (personal communication, 2001).

Coté, O. R.

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

Dalaudier, F.

C. Cot, F. Dalaudier, and A. Hauchecorne, Service d'Aéronomie du CNRS, BP 3, 91371 Verrières Le Buisson Cedex (personal communication, 2001).

de Leeuw, G.

Diehl, H.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Dobosy, R. J.

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

Fernald, F. G.

Gage, S.

S. Gage, “Creating a unified graphical wind turbulence model from multiple specifications,” in American Institute of Aeronautics and Astronautics (AIAA) 2003 Modeling and Simulation Technologies Conference and Exhibit (AIAA, 2003), paper 5529.

Gatt, P.

S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.

Hacker, J. M.

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

Hauchecorne, A.

C. Cot, F. Dalaudier, and A. Hauchecorne, Service d'Aéronomie du CNRS, BP 3, 91371 Verrières Le Buisson Cedex (personal communication, 2001).

Henderson, S.

S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.

Huffaker, R. M.

S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.

Jelalian, A. V.

A. V. Jelalian, “Detection probabilities and false alarm rates,” in Laser Radar Systems (Artech House, 1992), pp. 77-119.

Jenaro-Rabadan, G.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Klett, J. D.

Kunz, G. J.

Mirand, P.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Navé, P.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Pistner, T.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Rees, D.

S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.

Rehm, W.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Reymond, M.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Rocadenbosch, F.

Schmitt, N.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

Soriano, C.

Wroblewski, D. E.

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

AIAA J. (1)

C. W. Campbell, “Monte Carlo turbulence simulation using rational approximation to Von Karman spectra,” AIAA J. 24, 62-66 (1986).
[CrossRef]

Appl. Opt. (5)

J. Atmos. Sci. (1)

D. E. Wroblewski, O. R. Coté, J. M. Hacker, and R. J. Dobosy, “Cliff-ramp patterns and Kelvin-Helmoltz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements,” J. Atmos. Sci. 64, 2521-2539 (2007).
[CrossRef]

Other (7)

C. Cot, F. Dalaudier, and A. Hauchecorne, Service d'Aéronomie du CNRS, BP 3, 91371 Verrières Le Buisson Cedex (personal communication, 2001).

A. Behrendt, “Temperature measurements with lidar,” in Lidar, Range-Resolved Optical Remote Sensing of the Atmosphere, C. Weitkamp, ed. (Springer, 2005), pp. 281-286.

S. Henderson, P. Gatt, D. Rees, and R. M. Huffaker, “Wind Lidar,” in Laser Remote Sensing, T. Fujii and T. Fukuchi, eds (CRC Press, 2005), pp. 469-722.

N. Schmitt, W. Rehm, T. Pistner, H. Diehl, P. Navé, G. Jenaro-Rabadan, P. Mirand, and M. Reymond, “Flight test of the AWIATOR airborne LIDAR turbulence sensor,” presented at the Coherent Laser Radar Conference, Snowmass, Colorado, 7 August 2007.

U. S. Military specification MIL-F-8785C (1980), paragraph 3.7 Atmospheric disturbances.

S. Gage, “Creating a unified graphical wind turbulence model from multiple specifications,” in American Institute of Aeronautics and Astronautics (AIAA) 2003 Modeling and Simulation Technologies Conference and Exhibit (AIAA, 2003), paper 5529.

A. V. Jelalian, “Detection probabilities and false alarm rates,” in Laser Radar Systems (Artech House, 1992), pp. 77-119.

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Figures (12)

Fig. 1
Fig. 1

Simplified block diagram showing the key functionality of the direct-detection lidar system. The beam of a frequency-tripled injection-seeded Nd:YAG laser is sent to the atmosphere through an emission telescope. The backscattered light is filtered and focused onto a detector.

Fig. 2
Fig. 2

Principle of accumulation of the backscattered light from the different laser shots. The sum of the lidar signal is computed over N s laser shots at a pulse repetition frequency (PRF) over a spatial window given by the resolution distance. The detection range is defined as the maximal distance for which the decision of the presence of turbulence can be taken. The turbulence arises from a strong horizontal wind vertical gradient, which leads to an eddy for which the vertical wind can be detected through the variation of temperature/density.

Fig. 3
Fig. 3

Example of computation of vertical velocity deduced from the lidar signal. (a) The input wind speed as a function of distance; the gray curve represents the input vertical velocity and the dashed-dotted curve represents the vertical velocity computed from the lidar signal. (b) The associated fluctuation of temperature. (c) The deduced backscattering coefficient. The gray curve is the input back-scattering coefficient deduced from the input vertical velocity. The dashed-dotted curve is the filtered backscattering coefficient deduced from the lidar signal with photon noise added. The axis of distance is defined for the last pulse integration.

Fig. 4
Fig. 4

Detection range as a function of the integration distance. An integration distance larger than 10 km no longer brings additional information, thus leading to a plateau in the detection range.

Fig. 5
Fig. 5

Detection range as a function of flight altitude for two probabilities of excess turbulence. The higher flight level leads to a shorter detection range due to the reduced backscattering coefficient.

Fig. 6
Fig. 6

Influence of the Brundt–Väisälä frequency on the correlation between the input vertical velocity and the vertical velocity computed from the lidar signal. The area with a higher Brundt–Väisälä frequency, in which turbulence is more frequent, leads to a higher detection range.

Fig. 7
Fig. 7

Detection range as a function of laser power (P) and detector efficiency (ρ).

Fig. 8
Fig. 8

Influence of integration distance on the correlation between the input vertical velocity and the vertical velocity computed from the lidar signal.

Fig. 9
Fig. 9

Histogram of the shift between lidar signals computed with or without turbulence normalized by the photon noise (black histogram is computed with turbulence and white histogram is computed without turbulence) with a probability of excess turbulence of 10 3 .

Fig. 10
Fig. 10

Probability of missed alarm as a function of the probability of false alarm for the detection of turbulence with a probability of excess turbulence of 10 3 and 10 4 for a detection range of 20 km .

Fig. 11
Fig. 11

Dependence of missed alarm probability for a constant false alarm probability as a function of altitude with a probability of excess turbulence of 10 3 and 10 4 for a detection range of 20 km .

Fig. 12
Fig. 12

Probability of missed alarm as a function of detection distance for a constant probability of false alarm (taken at 10 3 ), for a probability of excess turbulence of 10 3 and a flight altitude of 6 km .

Tables (2)

Tables Icon

Table 1 Turbulence Intensities Taken into Account for the Computation

Tables Icon

Table 2 Lidar Characteristics Used in the Reference Case

Equations (17)

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Φ w ( ω ) = σ w 2 L w π V a 1 + 8 3 ( 1.339 L w ω V a ) 2 [ 1 + ( 1.339 L w ω V a ) 2 ] 11 6 ,
Φ w ( ω ) = H w ( ω )   conj ( H w ( ω ) ) ,
H w ( ω ) = σ w 2 L w π V a 1 + 2.7478 j L w ω V a 0.3398 ( L w ω V a ) 2 1 + 2.9958 j L w ω V a 1.9754 ( L w ω V a ) 2 0.1539 j ( L w ω V a ) 3 .
N = g θ θ z ,
δ ρ ( x ) ρ = δ T ( x ) T = N 2 g δ z .
δ ρ ( x ) ρ = δ T ( x ) T = N g w ( x ) .
α m ( x ) = N 0 σ R P ( z ) T 0 P 0 ( T ( z ) + δ T ( x ) ) ,
S ( x ) = P T int λ T 1 T 2 τ ρ h Σ i π R 2 2 ( x i V a F ) 2 ( K a α a + 3 8 π α m ( x i V a F ) ) exp [ 2 0 x i V a F ( α a + α m ( z ) ) d z ] ,
S ( x ) P T int λ T 1 T 2 τ ρ h Σ i π R 2 2 ( x i V a F ) 2 ( K a α a + 3 8 α m ( x i V a F ) ) exp [ 2 0 x i V a F ( α a + α m 0 ) d z ] + B ,
α m 0 = N 0 σ R P ( z ) T 0 P 0 T ( z ) .
S 0 ( x ) P T int λ T 1 T 2 τ ρ h Σ i π R 2 2 ( x i V a F ) 2 ( K a α a + 3 8 π α m 0 ) exp [ 2 0 x i V a F ( α a + α m 0 ) d z ] .
α ^ m ( x ) = α m 0 S ( x ) S 0 ( x ) + K a α a ( S ( x ) S 0 ( x ) 1 ) α m 0 S ( x ) S 0 ( x ) .
w ^ ( x ) = g N δ T ^ ( x ) T = g N ( 1 α m 0 α ^ m ( x ) ) g N ( 1 S 0 ( x ) S ( x ) ) .
1 π σ T exp ( ( x m T σ T ) 2 ) ,
1 π σ C exp ( ( x m c σ c ) 2 ) .
P FA = 1 2 erfc ( Threshold m c σ c ) ,
P MA = 1 1 2 erfc ( Threshold m T σ T ) .

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