Abstract

The conventional method of calculating atmospheric temperature profiles using Rayleigh-scattering lidar measurements has limitations that necessitate abandoning temperatures retrieved at the greatest heights, due to the assumption of a pressure value required to initialize the integration at the highest altitude. An inversion approach is used to develop an alternative way of retrieving nightly atmospheric temperature profiles from the lidar measurements. Measurements obtained by the Purple Crow lidar facility located near The University of Western Ontario are used to develop and test this new technique. Our results show temperatures can be reliably retrieved at all heights where measurements with adequate signal-to-noise ratio exist. A Monte Carlo technique was developed to provide accurate estimates of both the systematic and random uncertainties for the retrieved nightly average temperature profile. An advantage of this new method is the ability to seed the temperature integration from the lowest rather than the greatest height, where the variability of the pressure is smaller than in the mesosphere or lower thermosphere and may in practice be routinely measured by a radiosonde, rather than requiring a rocket or satellite-borne measurement. Thus, this new technique extends the altitude range of existing Rayleigh-scatter lidars 10–15 km, producing the equivalent of four times the power-aperture product.

© 2012 Optical Society of America

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References

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  1. A. Hauchecorne and M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 7, 565–568 (1980).
    [CrossRef]
  2. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).
  3. P. C. Mahalanobis, “On the generalized distance in statistics,” Proc. Natl. Inst. Sci. India 2, 49–55 (1936).
  4. V. A. Kovalev and W. E. Eichinger, Elastic Lidar: Theory, Practice and Analysis Method (Wiley, 2004).
  5. P. B. Russell and B. M. Morley, “Orbiting lidar simulations. 2: density, temperature, aerosol, and cloud measurements by a wavelength combining technique,” Appl. Opt. 21, 1554–1563 (1982).
    [CrossRef]
  6. J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
    [CrossRef]
  7. R. J. Sica, S. Sargoytchev, P. S. Argall, E. F. Borra, L. Girard, C. T. Sparrow, and S. Flatt, “Lidar measurements taken with a large-aperture liquid mirror. 1. Rayleigh-scatter system,” Appl. Opt. 34, 6925–6936 (1995).
    [CrossRef]
  8. E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).
  9. P. S. Argall and R. J. Sica, “A comparison of Rayleigh and sodium lidar temperature climatologies,” Ann. Geophys. 25, 27–35 (2007).
    [CrossRef]
  10. JCGM, “Evaluation of measurement data: guide to the expression of uncertainty in measurement,” Tech. Rep. (Joint Committee for Guides in Meteorology, 2008).
  11. JCGM, “Evaluation of measurement data,” supplement 1 to the “Guide to the expression of uncertainty in measurement propagation of distributions using a Monte Marlo method,” Tech. Rep. (Joint Committee for Guides in Meteorology, 2008).
  12. R. W. Hamming, Digital Filters (Prentice-Hall, 1977).

2007 (1)

P. S. Argall and R. J. Sica, “A comparison of Rayleigh and sodium lidar temperature climatologies,” Ann. Geophys. 25, 27–35 (2007).
[CrossRef]

1997 (1)

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

1995 (1)

1990 (1)

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

1982 (1)

1980 (1)

A. Hauchecorne and M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

1936 (1)

P. C. Mahalanobis, “On the generalized distance in statistics,” Proc. Natl. Inst. Sci. India 2, 49–55 (1936).

Argall, P. S.

Barnett, J. J.

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).

Borra, E. F.

Chandra, S.

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

Chanin, M. L.

A. Hauchecorne and M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Corney, M.

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

Eichinger, W. E.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar: Theory, Practice and Analysis Method (Wiley, 2004).

Flatt, S.

Fleming, E. L.

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

Girard, L.

Hamming, R. W.

R. W. Hamming, Digital Filters (Prentice-Hall, 1977).

Hauchecorne, A.

A. Hauchecorne and M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Heinselman, C. J.

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Kovalev, V. A.

V. A. Kovalev and W. E. Eichinger, Elastic Lidar: Theory, Practice and Analysis Method (Wiley, 2004).

Mahalanobis, P. C.

P. C. Mahalanobis, “On the generalized distance in statistics,” Proc. Natl. Inst. Sci. India 2, 49–55 (1936).

Morley, B. M.

Nielsen, N. B.

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).

Russell, P. B.

Sargoytchev, S.

Sica, R. J.

Sohn, J.

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Sparrow, C. T.

Thayer, J. P.

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Warren, R. E.

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Adv. Space Res. (1)

E. L. Fleming, S. Chandra, J. J. Barnett, and M. Corney, “Zonal mean temperature, pressure, zonal wind and geopotential height as functions of latitude,” Adv. Space Res. 12, 11–59 (1990).

Ann. Geophys. (1)

P. S. Argall and R. J. Sica, “A comparison of Rayleigh and sodium lidar temperature climatologies,” Ann. Geophys. 25, 27–35 (2007).
[CrossRef]

Appl. Opt. (2)

Geophys. Res. Lett. (1)

A. Hauchecorne and M. L. Chanin, “Density and temperature profiles obtained by lidar between 35 and 70 km,” Geophys. Res. Lett. 7, 565–568 (1980).
[CrossRef]

Opt. Eng. (1)

J. P. Thayer, N. B. Nielsen, R. E. Warren, C. J. Heinselman, and J. Sohn, “Rayleigh lidar system for middle atmosphere research in the arctic,” Opt. Eng. 36, 2045–2061 (1997).
[CrossRef]

Proc. Natl. Inst. Sci. India (1)

P. C. Mahalanobis, “On the generalized distance in statistics,” Proc. Natl. Inst. Sci. India 2, 49–55 (1936).

Other (5)

V. A. Kovalev and W. E. Eichinger, Elastic Lidar: Theory, Practice and Analysis Method (Wiley, 2004).

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).

JCGM, “Evaluation of measurement data: guide to the expression of uncertainty in measurement,” Tech. Rep. (Joint Committee for Guides in Meteorology, 2008).

JCGM, “Evaluation of measurement data,” supplement 1 to the “Guide to the expression of uncertainty in measurement propagation of distributions using a Monte Marlo method,” Tech. Rep. (Joint Committee for Guides in Meteorology, 2008).

R. W. Hamming, Digital Filters (Prentice-Hall, 1977).

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Figures (6)

Fig. 1.
Fig. 1.

Temperature retrievals using the CH method for the Rayleigh-scatter lidar measurements on 1 September 2005. These retrievals show the effect of varying the choice of the top seed pressure. The right panel shows the temperature differences from the profile retrieved using the original seed pressures given in the text.

Fig. 2.
Fig. 2.

Temperature retrievals using an inversion approach for PCL Rayleigh-scatter lidar measurements on 1 September 2005. These retrievals show the effect of varying the choice of the top seed pressure. The right panel shows the temperature differences from the profile retrieved using the original seed pressures given in the text.

Fig. 3.
Fig. 3.

Comparison of the statistical uncertainties reported for the night of 1 September 2005 for the CH method and an inversion approach from Figs. 1 and 2 respectively with no variation in seed pressure. The uncertainties with the Grid Search method were found using the Monte Carlo approach described in Section 5.

Fig. 4.
Fig. 4.

Temperature retrieval from an inversion approach for August 2000. There were a total of 270 one-minute scans for this night. The vertical resolution is 500 m. The red portion of the plot indicates the extra temperature measurements gained when compared to the CH method where the top 10–15 km would have an unacceptably high systematic uncertainty.

Fig. 5.
Fig. 5.

Temperature retrieval from an inversion approach for 22 August 1995, using 483 one-minute scans, in the same format as Fig. 4.

Fig. 6.
Fig. 6.

Temperature retrieval from an inversion approach for 5 May 2006, using 385 one-minute scans, in the same format as Fig. 4.

Equations (17)

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Ti=P0MRρi+MRziz0ρ(z)g(z)ρidz,
Ti=Ttrue+ΔT,
Ttrue=MPtrueRρi+MRziz0ρ(z)g(z)ρidz,
ΔT=MΔPRρi.
F(m)=d,
χ2(X)=(XX¯)TVar1(XX¯).
χ2(x)=1Nj=1N(xjxj¯)2σj2.
χ2=(XexpXmodel)TCov1(XexpXmodel),
Cov(xi,xj)=k=1M(xi,kxi¯)(xj,kxj¯)M.
z0zidPP(z)=MRz0zig(z)T(z)dz,
P(zi)=P0exp(MRz0zig(z)T(z)dz),
ρ(zi)RT(zi)M=P0exp(MRz0zig(z)T(z)dz).
ρ(zi)=C(N(zi)B(zi))zi2.
N(zi)=P0MCRzi2T(zi)exp(MRz0zig(z)T(z)dz).
N(zi)=P0MN0ρ0RT(zi)exp(MRz0zig(z)T(z)dz),=T0N0T(zi)exp(MRz0zig(z)T(z)dz).
σNmodel(z)2=N(z)+NBG(z).
NMC(z)=N(z)+σN(z)λ,

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