Abstract

The measurement of temperature in the middle atmosphere with Rayleigh-scatter lidars is an important technique for assessing atmospheric change. Current retrieval schemes for this temperature have several shortcomings, which can be overcome by using an optimal estimation method (OEM). Forward models are presented that completely characterize the measurement and allow the simultaneous retrieval of temperature, dead time, and background. The method allows a full uncertainty budget to be obtained on a per profile basis that includes, in addition to the statistical uncertainties, the smoothing error and uncertainties due to Rayleigh extinction, ozone absorption, lidar constant, nonlinearity in the counting system, variation of the Rayleigh-scatter cross section with altitude, pressure, acceleration due to gravity, and the variation of mean molecular mass with altitude. The vertical resolution of the temperature profile is found at each height, and a quantitative determination is made of the maximum height to which the retrieval is valid. A single temperature profile can be retrieved from measurements with multiple channels that cover different height ranges, vertical resolutions, and even different detection methods. The OEM employed is shown to give robust estimates of temperature, which are consistent with previous methods, while requiring minimal computational time. This demonstrated success of lidar temperature retrievals using an OEM opens new possibilities in atmospheric science for measurement integration between active and passive remote sensing instruments.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  11. R. J. Sica and P. S. Argall, “Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar,” Ann. Geophys. 25, 2139–2145 (2007).
    [Crossref]
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    [Crossref]
  13. R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. A. E. Hedin, “Extension of the MSIS thermosphere model into the middle and lower atmosphere,” J. Geophys. Res. Atmos. 96, 1159–1172 (1991).
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  26. M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
    [Crossref]

2014 (1)

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

2012 (1)

2008 (2)

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

2007 (4)

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

R. J. Sica and P. S. Argall, “Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar,” Ann. Geophys. 25, 2139–2145 (2007).
[Crossref]

R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
[Crossref]

P. S. Argall, “Upper altitude limit for Rayleigh lidar,” Annales Geophysicae 25, 19–25 (2007).
[Crossref]

2005 (2)

P. Eriksson, C. Jiménez, and S. A. Buehler, “Qpack, a general tool for instrument simulation and retrieval work,” J. Quant. Spectrosc. Radiat. Transfer 91, 47–64 (2005).
[Crossref]

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

2004 (1)

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

2001 (1)

R. J. Sica, Z. A. Zylawy, and P. S. Argall, “Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere,” J. Atmos. Ocean. Technol. 18, 1223–1228 (2001).
[Crossref]

1996 (1)

R. Sica and M. Thorsley, “Measurements of superadiabatic lapse rates in the middle atmosphere,” Geophys. Res. Lett. 23, 2797–2800 (1996).
[Crossref]

1995 (1)

1994 (1)

R. T. Clancy, D. W. Rusch, and M. T. Callan, “Temperature minima in the average thermal structure of the middle mesosphere (70–80  km) from analysis of 40 to 92  km SME global temperature profiles,” J. Geophys. Res. Atmos. 99, 19001–19020 (1994).
[Crossref]

1993 (2)

P. Keckhut, A. Hauchecorne, and M. L. Chanin, “A critical review of the database acquired for the long-term surveillance of the middle atmosphere by the French Rayleigh lidars,” J. Atmos. Ocean. Technol. 10, 850–867 (1993).
[Crossref]

D. P. Donovan, J. A. Whiteway, and A. I. Carswell, “Correction for nonlinear photon-counting effects in lidar systems,” Appl. Opt. 32, 6742–6753 (1993).
[Crossref]

1991 (2)

A. E. Hedin, “Extension of the MSIS thermosphere model into the middle and lower atmosphere,” J. Geophys. Res. Atmos. 96, 1159–1172 (1991).
[Crossref]

A. Hauchecorne, M.-L. Chanin, and P. Keckhut, “Climatology and trends of the middle atmospheric temperature (33–87  km) as seen by Rayleigh lidar over the south of France,” J. Geophys. Res. Atmos. 96, 15297–15309 (1991).
[Crossref]

1984 (1)

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[Crossref]

1980 (1)

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

1968 (1)

M. Griggs, “Absorption coefficients of ozone in the ultraviolet and visible regions,” J. Chem. Phys. 49, 857–859 (1968).
[Crossref]

Agnew, J. L.

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

Alpers, M.

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

Argall, P. S.

P. S. Argall, “Upper altitude limit for Rayleigh lidar,” Annales Geophysicae 25, 19–25 (2007).
[Crossref]

R. J. Sica and P. S. Argall, “Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar,” Ann. Geophys. 25, 2139–2145 (2007).
[Crossref]

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

R. J. Sica, Z. A. Zylawy, and P. S. Argall, “Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere,” J. Atmos. Ocean. Technol. 18, 1223–1228 (2001).
[Crossref]

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]

Bandoro, J.

Barnett, J. J.

J. J. Barnett and M. Corney, “Middle atmosphere reference model from satellite data,” in International Council of Scientific Unions Middle Atmosphere Program, Handbook for MAP (SCOSTEP, 1985), Vol. 16, pp. 47–85.

Beatty, T. J.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Bills, R. E.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Boone, C. D.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Borra, E. F.

Buehler, S. A.

P. Eriksson, C. Jiménez, and S. A. Buehler, “Qpack, a general tool for instrument simulation and retrieval work,” J. Quant. Spectrosc. Radiat. Transfer 91, 47–64 (2005).
[Crossref]

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

Callan, M. T.

R. T. Clancy, D. W. Rusch, and M. T. Callan, “Temperature minima in the average thermal structure of the middle mesosphere (70–80  km) from analysis of 40 to 92  km SME global temperature profiles,” J. Geophys. Res. Atmos. 99, 19001–19020 (1994).
[Crossref]

Carswell, A. I.

Chanin, M.

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

Chanin, M. L.

P. Keckhut, A. Hauchecorne, and M. L. Chanin, “A critical review of the database acquired for the long-term surveillance of the middle atmosphere by the French Rayleigh lidars,” J. Atmos. Ocean. Technol. 10, 850–867 (1993).
[Crossref]

Chanin, M.-L.

A. Hauchecorne, M.-L. Chanin, and P. Keckhut, “Climatology and trends of the middle atmospheric temperature (33–87  km) as seen by Rayleigh lidar over the south of France,” J. Geophys. Res. Atmos. 96, 15297–15309 (1991).
[Crossref]

Clancy, R. T.

R. T. Clancy, D. W. Rusch, and M. T. Callan, “Temperature minima in the average thermal structure of the middle mesosphere (70–80  km) from analysis of 40 to 92  km SME global temperature profiles,” J. Geophys. Res. Atmos. 99, 19001–19020 (1994).
[Crossref]

Corney, M.

J. J. Barnett and M. Corney, “Middle atmosphere reference model from satellite data,” in International Council of Scientific Unions Middle Atmosphere Program, Handbook for MAP (SCOSTEP, 1985), Vol. 16, pp. 47–85.

Daffer, W. H.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Donovan, D. P.

Eixmann, R.

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

Eriksson, P.

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

P. Eriksson, C. Jiménez, and S. A. Buehler, “Qpack, a general tool for instrument simulation and retrieval work,” J. Quant. Spectrosc. Radiat. Transfer 91, 47–64 (2005).
[Crossref]

Flatt, S.

Fricke-Begemann, C.

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

Gardner, C. S.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Gerding, M.

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

Girard, L.

Grainger, R. G.

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

Griggs, M.

M. Griggs, “Absorption coefficients of ozone in the ultraviolet and visible regions,” J. Chem. Phys. 49, 857–859 (1968).
[Crossref]

Hauchecorne, A.

P. Keckhut, A. Hauchecorne, and M. L. Chanin, “A critical review of the database acquired for the long-term surveillance of the middle atmosphere by the French Rayleigh lidars,” J. Atmos. Ocean. Technol. 10, 850–867 (1993).
[Crossref]

A. Hauchecorne, M.-L. Chanin, and P. Keckhut, “Climatology and trends of the middle atmospheric temperature (33–87  km) as seen by Rayleigh lidar over the south of France,” J. Geophys. Res. Atmos. 96, 15297–15309 (1991).
[Crossref]

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

Hedin, A. E.

A. E. Hedin, “Extension of the MSIS thermosphere model into the middle and lower atmosphere,” J. Geophys. Res. Atmos. 96, 1159–1172 (1991).
[Crossref]

Hoffner, J.

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

Höffner, J.

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

Hostetler, C.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Jiménez, C.

P. Eriksson, C. Jiménez, and S. A. Buehler, “Qpack, a general tool for instrument simulation and retrieval work,” J. Quant. Spectrosc. Radiat. Transfer 91, 47–64 (2005).
[Crossref]

Keckhut, P.

P. Keckhut, A. Hauchecorne, and M. L. Chanin, “A critical review of the database acquired for the long-term surveillance of the middle atmosphere by the French Rayleigh lidars,” J. Atmos. Ocean. Technol. 10, 850–867 (1993).
[Crossref]

A. Hauchecorne, M.-L. Chanin, and P. Keckhut, “Climatology and trends of the middle atmospheric temperature (33–87  km) as seen by Rayleigh lidar over the south of France,” J. Geophys. Res. Atmos. 96, 15297–15309 (1991).
[Crossref]

Khanna, J.

Kuhn, T.

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

Labow, G. J.

R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
[Crossref]

Lambert, A.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Lautenbach, J.

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

Livesey, N. J.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Logan, J. A.

R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
[Crossref]

Lübken, F. J.

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

Manney, G. L.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

McElroy, C. T.

McPeters, R. D.

R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
[Crossref]

Mlynczak, M. G.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Nicolet, M.

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[Crossref]

Pawson, S.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Peters, D. M.

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

Povey, A. C.

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

Rauthe, M.

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

Read, W. G.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
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Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Theory and Practice (World Scientific, 2011).

Rusch, D. W.

R. T. Clancy, D. W. Rusch, and M. T. Callan, “Temperature minima in the average thermal structure of the middle mesosphere (70–80  km) from analysis of 40 to 92  km SME global temperature profiles,” J. Geophys. Res. Atmos. 99, 19001–19020 (1994).
[Crossref]

Russell, J. M.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Santee, M. L.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Sargoytchev, S.

Schwartz, M. J.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Senft, D. C.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Sica, R.

R. Sica and M. Thorsley, “Measurements of superadiabatic lapse rates in the middle atmosphere,” Geophys. Res. Lett. 23, 2797–2800 (1996).
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Sica, R. J.

J. Khanna, J. Bandoro, R. J. Sica, and C. T. McElroy, “New technique for retrieval of atmospheric temperature profiles from Rayleigh-scatter lidar measurements using nonlinear inversion,” Appl. Opt. 51, 7945–7952 (2012).
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R. J. Sica and P. S. Argall, “Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar,” Ann. Geophys. 25, 2139–2145 (2007).
[Crossref]

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

R. J. Sica, Z. A. Zylawy, and P. S. Argall, “Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere,” J. Atmos. Ocean. Technol. 18, 1223–1228 (2001).
[Crossref]

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).
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Sparrow, C. T.

Thorsley, M.

R. Sica and M. Thorsley, “Measurements of superadiabatic lapse rates in the middle atmosphere,” Geophys. Res. Lett. 23, 2797–2800 (1996).
[Crossref]

Verdes, C.

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

von Engeln, A.

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

Walker, K. A.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Whiteway, J. A.

Wu, D. L.

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

Zylawy, Z. A.

R. J. Sica, Z. A. Zylawy, and P. S. Argall, “Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere,” J. Atmos. Ocean. Technol. 18, 1223–1228 (2001).
[Crossref]

Ann. Geophys. (1)

R. J. Sica and P. S. Argall, “Seasonal and nightly variations of gravity-wave energy density in the middle atmosphere measured by the Purple Crow Lidar,” Ann. Geophys. 25, 2139–2145 (2007).
[Crossref]

Annales Geophysicae (2)

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

P. S. Argall, “Upper altitude limit for Rayleigh lidar,” Annales Geophysicae 25, 19–25 (2007).
[Crossref]

Appl. Opt. (3)

Atmos. Chem. Phys. (2)

M. Alpers, R. Eixmann, C. Fricke-Begemann, M. Gerding, and J. Hoffner, “Temperature lidar measurements from 1 to 105  km altitude using resonance, Rayleigh, and rotational Raman scattering,” Atmos. Chem. Phys. 4, 793–800 (2004).
[Crossref]

M. Gerding, J. Höffner, J. Lautenbach, M. Rauthe, and F. J. Lübken, “Seasonal variation of nocturnal temperatures between 1 and 105  km altitude at 54° N observed by lidar,” Atmos. Chem. Phys. 8, 7465–7482 (2008).
[Crossref]

Atmos. Meas. Tech. (1)

A. C. Povey, R. G. Grainger, D. M. Peters, and J. L. Agnew, “Retrieval of aerosol backscatter, extinction, and lidar ratio from Raman lidar with optimal estimation,” Atmos. Meas. Tech. 7, 757–776 (2014).
[Crossref]

Geophys. Res. Lett. (2)

R. Sica and M. Thorsley, “Measurements of superadiabatic lapse rates in the middle atmosphere,” Geophys. Res. Lett. 23, 2797–2800 (1996).
[Crossref]

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

J. Atmos. Ocean. Technol. (2)

P. Keckhut, A. Hauchecorne, and M. L. Chanin, “A critical review of the database acquired for the long-term surveillance of the middle atmosphere by the French Rayleigh lidars,” J. Atmos. Ocean. Technol. 10, 850–867 (1993).
[Crossref]

R. J. Sica, Z. A. Zylawy, and P. S. Argall, “Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere,” J. Atmos. Ocean. Technol. 18, 1223–1228 (2001).
[Crossref]

J. Chem. Phys. (1)

M. Griggs, “Absorption coefficients of ozone in the ultraviolet and visible regions,” J. Chem. Phys. 49, 857–859 (1968).
[Crossref]

J. Geophys. Res. (1)

M. J. Schwartz, A. Lambert, G. L. Manney, W. G. Read, N. J. Livesey, C. D. Boone, W. H. Daffer, M. G. Mlynczak, S. Pawson, J. M. Russell, M. L. Santee, K. A. Walker, and D. L. Wu, “Validation of the aura microwave limb sounder temperature and geopotential height measurements,” J. Geophys. Res. 113, 1–23 (2008).
[Crossref]

J. Geophys. Res. Atmos. (4)

A. Hauchecorne, M.-L. Chanin, and P. Keckhut, “Climatology and trends of the middle atmospheric temperature (33–87  km) as seen by Rayleigh lidar over the south of France,” J. Geophys. Res. Atmos. 96, 15297–15309 (1991).
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A. E. Hedin, “Extension of the MSIS thermosphere model into the middle and lower atmosphere,” J. Geophys. Res. Atmos. 96, 1159–1172 (1991).
[Crossref]

R. D. McPeters, G. J. Labow, and J. A. Logan, “Ozone climatological profiles for satellite retrieval algorithms,” J. Geophys. Res. Atmos. 112, D05308 (2007).
[Crossref]

R. T. Clancy, D. W. Rusch, and M. T. Callan, “Temperature minima in the average thermal structure of the middle mesosphere (70–80  km) from analysis of 40 to 92  km SME global temperature profiles,” J. Geophys. Res. Atmos. 99, 19001–19020 (1994).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (2)

P. Eriksson, C. Jiménez, and S. A. Buehler, “Qpack, a general tool for instrument simulation and retrieval work,” J. Quant. Spectrosc. Radiat. Transfer 91, 47–64 (2005).
[Crossref]

S. A. Buehler, P. Eriksson, T. Kuhn, A. von Engeln, and C. Verdes, “ARTS, the atmospheric radiative transfer simulator,” J. Quant. Spectrosc. Radiat. Transfer 91, 65–93 (2005).
[Crossref]

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M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[Crossref]

Other (4)

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Theory and Practice (World Scientific, 2011).

J. J. Barnett and M. Corney, “Middle atmosphere reference model from satellite data,” in International Council of Scientific Unions Middle Atmosphere Program, Handbook for MAP (SCOSTEP, 1985), Vol. 16, pp. 47–85.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, and C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study Handbook (SCOSTEP, 1989), Vol. 2, pp. 1–40.

Committee on Extension to the Standard Atmosphere, “US standard atmosphere, 1976,” (National Oceanic and Atmospheric Administration, 1976).

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Figures (24)

Fig. 1.
Fig. 1. Temperature Jacobians, normalized to the number density (left panel) and averaging kernels (right panel) for a synthetic measurement using the HSEQ forward model. The horizontal dashed line on the right panel is the height above which the a priori temperature profile makes a significant contribution to the retrieval. This height is determined from the trace of the averaging kernel matrix.
Fig. 2.
Fig. 2. Representative temperature Jacobian at 45 km altitude for the HSEQ forward model (blue curve) and the LE forward model (red curve).
Fig. 3.
Fig. 3. Vertical resolution of the retrieval for a synthetic measurement using the HSEQ forward model. The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 4.
Fig. 4. Residuals between the HSEQ forward model and synthetic measurements.
Fig. 5.
Fig. 5. Temperature retrieval from synthetic measurements using the HSEQ forward model. The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 6.
Fig. 6. Uncertainty budget for the HSEQ forward model synthetic temperature retrieval. Left panel: Statistical (blue), smoothing (red), pressure (yellow circle), lidar constant (magenta x), ozone density (green +), ozone cross section (blue *), density profile for Rayleigh extinction (red square), Rayleigh extinction cross section (blue diamond), dead time (orange triangle), variation of Rayleigh-scatter cross section with height (yellow triangle), variation of mean molecular mass with height (purple triangle), gravity (green triangle), and total uncertainty (black line). The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval. Right panel: Expanded view of the uncertainties in the stratosphere.
Fig. 7.
Fig. 7. Temperature Jacobians, normalized to the number density (left panel) and averaging kernels (right panel) for a synthetic measurement using the LE forward model. The horizontal dashed line on the right panel is the height above which the a priori temperature profile makes a significant contribution to the retrieval. This height is determined from the trace of the averaging kernel matrix.
Fig. 8.
Fig. 8. Vertical resolution of the retrieval for a synthetic measurement using the LE forward model. The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 9.
Fig. 9. Residuals between the LE forward model and the synthetic measurements.
Fig. 10.
Fig. 10. Temperature retrieval from synthetic measurements using the LE forward model. The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 11.
Fig. 11. Uncertainty budget for the LE forward model synthetic temperature retrieval. Left panel: Statistical (blue), smoothing (red), pressure (yellow circle), lidar constant (magenta x), ozone density (green +), ozone cross section (blue *), density profile for Rayleigh extinction (red square), Rayleigh extinction cross section (blue diamond), dead time (orange triangle), and the variation of Rayleigh-scatter cross section with height (yellow triangle) and total uncertainty (black line). The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval. Right panel: Expanded view of the uncertainties in the stratosphere.
Fig. 12.
Fig. 12. Temperature retrieval using the HSEQ forward model for a synthetic measurement, which includes a gravity-wave-like disturbance with a 10 km vertical wavelength. Left panel: Temperature profile. Right panel: Temperature difference between the retrieved and the true profiles (blue curve) and between the retrieved and a priori profiles (red curve). The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 13.
Fig. 13. Temperature retrieval using the HSEQ forward model for a synthetic measurement, which includes a gravity-wave-like disturbance with a 3 km vertical wavelength. Left panel: Temperature profile. Right panel: Temperature difference between the retrieved and the true profiles (blue curve) and between the retrieved and a priori profiles (red curve). The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 14.
Fig. 14. Single channel HSEQ temperature retrieval from Purple Crow Lidar measurements on 24 May 2012 (red curve). The blue curve uses the same photocount profile to retrieve temperature using the HC method. The a priori temperature profile (cyan curve) is the US standard atmosphere. The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 15.
Fig. 15. Uncertainty budget for the HSEQ forward model temperature retrieval on 24 May 2012. Left panel: Statistical (blue), smoothing (red), pressure (yellow circle), lidar constant (magenta x), ozone density (green +), ozone cross section (blue *), density profile for Rayleigh extinction (red square), Rayleigh extinction cross section (blue diamond), dead time (orange triangle), variation of Rayleigh-scatter cross section with height (yellow triangle), variation of mean molecular mass with height (purple triangle), gravity (green triangle), and total uncertainty (black line). The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval. Right panel: Expanded view of the uncertainties in the stratosphere.
Fig. 16.
Fig. 16. Pressure percentage difference on 24 May 2012 for the CIRA-86 model (blue curve), pressure calculated from the temperature assuming HSEQ (red curve), and the MLS pressure profile (green curve) relative to the US standard model pressure.
Fig. 17.
Fig. 17. HLR and LLR digital channel photocount measurements from the night of 24 May 2012. The count rates are typical for the PCL Rayleigh-scatter system.
Fig. 18.
Fig. 18. Temperature Jacobians, normalized to the number density for the LLR and HLR channels using the HSEQ forward model on 24 May 2012.
Fig. 19.
Fig. 19. Averaging kernels (left panel) and vertical resolution for the two channel retrieval on 24 May 2012 using the HSEQ forward model. The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 20.
Fig. 20. Residuals between the two-channel photocount measurements with the HSEQ forward model. The LLR measurements contribute primarily below 37.5 km, the HLR measurements above 37.5 km.
Fig. 21.
Fig. 21. Two-channel HSEQ temperature retrieval from Purple Crow Lidar measurements on 24 May 2012 (red curve). The blue and green curve uses the HLR and LLR photocount profile, respectively, to retrieve temperature using the HC method. The a priori temperature profile (cyan curve) is the US Standard Atmosphere. The horizontal dotted line is the height above which the a priori temperature profile makes a significant contribution to the retrieval.
Fig. 22.
Fig. 22. Uncertainty budget for the HSEQ forward model two-channel temperature retrieval on 24 May 2012. Left panel: statistical (blue), smoothing (red), pressure (yellow circle), lidar constant (magenta x), ozone density (green +), ozone cross section (blue *), density profile for Rayleigh extinction (red square), Rayleigh extinction cross section (blue diamond), variation of Rayleigh-scatter cross section with height (orange triangle), variation of mean molecular mass with height (yellow triangle), gravity (purple triangle), and total uncertainty (black line). The horizontal dashed line is the height above which the a priori temperature profile makes a significant contribution to the retrieval. Right panel: Expanded view of the uncertainties in the stratosphere.
Fig. 23.
Fig. 23. Comparison of the OEM two-channel retrieval in the stratosphere (red curve) to single-channel profiles calculated from the HC method for the HLR and LLRd channels (blue and green curves) on 24 May 2012 and 07 August 2012, highlighting the differences in retrieved temperature profiles in the merging region. The cyan curve in both figures is the a priori temperature profile.
Fig. 24.
Fig. 24. Temperature retrieval (red curve) using two digital channels for nine nights of measurements. The blue curve shows the HC method retrieval for the same measurements using the HLR channel; the green curve is for the LLR channel. The temperatures from the HC method have been cut off at the height where the variance becomes greater than 10%. The shaded areas indicate the ±1σ uncertainty including smoothing and statistical uncertainty for the OEM retrieval and the statistical uncertainties for the HC method.

Equations (23)

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Nt(z)=ψ(z)·n(z)z2+B,
No=NteNtγ,
dpdz=g(z)ρ(z),
ψ(z)=C·σR(z)·e2·τO3(z)·e2·τR(z).
τO3(z)=0znO3(z)·σO3(z)dz.
τR(z)=0zn(z)·σR(z)dz.
No=p0ψ*z21T(z)·exp{M*Rzztopg(z)T(z)dz}+B,
y=F(x,b)+ϵ,
cost=[yF(x^,b)]TSy1[yF(x^,b)]+[x^xa]TSa1[x^xa].
Kx=Fx.
Gy=x^y.
A=x^x=GyKx.
Sm=GySyGyT.
Ss=(AIn)Se(AIn)T.
Se=KbSbKbT+Sy,
SF=GyKbSbKbTGyT.
Stotal=Sm+Ss+SF.
No(z)=ψ(z)z2p(z)kT(z)+B.
Nt(z)=ψ(z)z2p(z)kT(z)+B,
No(z)=NteNtγ.
Nt=ψ(z)z2phseq(z)kT(z)+B,
phseq(z)=p0exp{1RzztopM(z)g(z)T(z)dz}.
No(z)=NteNtγ.

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