Abstract

The performance of a spaceborne temperature lidar based on the pure rotational Raman (RR) technique in the UV has been simulated. Results show that such a system deployed onboard a low-Earth-orbit satellite would provide global-scale clear-sky temperature measurements in the troposphere and lower stratosphere with precisions that satisfy World Meteorological Organization (WMO) threshold observational requirements for numerical weather prediction and climate research applications. Furthermore, nighttime temperature measurements would still be within the WMO threshold observational requirements in the presence of several cloud structures. The performance of aerosol extinction measurements from space, which can be carried out simultaneously with temperature measurements by RR lidar, is also assessed. Furthermore, we discuss simulations of relative humidity measurements from space obtained from RR temperature measurements and water-vapor data measured with the differential absorption lidar (DIAL) technique.

© 2006 Optical Society of America

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Corrections

Paolo Di Girolamo, Andreas Behrendt, and Volker Wulfmeyer, "Spaceborne profiling of atmospheric temperature and particle extinction with pure rotational Raman lidar and of relative humidity in combination with differential absorption lidar: performance simulations--erratum," Appl. Opt. 45, 4909-4909 (2006)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-45-20-4909

References

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2005 (2)

F. Karbou, F. Aires, C. Prigent, and L. Eymard, "Potential of Advanced Microwave Sounding Unit-A (AMSU-A) and AMSU-B measurements for atmospheric temperature and humidity profiling over land," J. Geophys. Res. 110, D07109, doi: (2005).
[CrossRef]

M. Ostermeyer, P. Kappe, R. Menzel, and V. Wulfmeyer, "Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation system," Appl. Opt. 44, 582-590 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
[CrossRef]

2002 (2)

2000 (2)

A. Behrendt and J. Reichardt, "Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interference-filter-based polychromator," Appl. Opt. 39, 1372-1378 (2000).
[CrossRef]

G. Ehret, H. H. Klingenberg, U. Hefter, A. Assion, A. Fix, G. Proberaj, S. Berger, S. Geiger, and Q. Lü, "High peak and average power all solid-state laser systems for airborne LIDAR applications," LaserOpto 32, 29-37 (2000).

1999 (3)

1998 (5)

V. Wulfmeyer, "Ground-based differential absorption lidar for water-vapor profiling: development and specifications of a high-performance laser transmitter," Appl. Opt. 37, 3804-3824 (1998).
[CrossRef]

J. Bösenberg, "Ground-based differential absorption lidar for water-vapor and temperature profiling: methodology," Appl. Opt. 37, 3845-3860 (1998).
[CrossRef]

U. Wandinger, "Multiple-scattering influence on extinction and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars," Appl. Opt. 37, 417-427 (1998).
[CrossRef]

W. F. Feltz, W. L. Smith, R. O. Knuteson, H. R. Revercomb, H. B. Howell, and H. H. Woolf, "Meteorological applications of temperature and water vapor retrievals from the ground-based Atmospheric Emitted Radiance Interferometer (AERI)," J. Appl. Meteorol. 37, 857-875 (1998).
[CrossRef]

T. Leblanc, I. S. McDermid, A. Hauchecorne, and P. Keckhut, "Evaluation of lidar temperature analysis algorithms using simulated data," J. Geophys. Res. 103, 6177-6187 (1998).

1993 (3)

D. Nedeljkovic, A. Hauchecorne, and M. L. Chanin, "Rotational Raman lidar to measure the atmospheric temperature from the ground," IEEE Trans. Geosci Remote Sens. 31, 90-101 (1993).
[CrossRef]

F. A. Theopold and J. Bösenberg, "Differential absorption lidar measurements of atmospheric temperature profiles: theory and experiment," J. Atmos. Oceanic Technol. 10, 165-179 (1993).
[CrossRef]

G. Vaughan, D. P. Wareing, S. J. Pepler, L. Thomas, and V. Mitev, "Atmospheric temperature profiles made by rotational Raman scattering," Appl. Opt. 32, 2758-2764 (1993).
[CrossRef] [PubMed]

1990 (2)

1987 (1)

1984 (1)

1983 (1)

1980 (2)

G. Mégie and R. T. Menzies, "Complementarity of UV and IR differential absorption lidar for global measurements of atmospheric species," Appl. Opt. 19, 1173-1183 (1980).
[CrossRef] [PubMed]

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]

1978 (1)

J. Marling, "1.05-1.44 μm tunability and performance of the CW Nd3+:YAG laser," IEEE J. Quantum Electron. QE-14, 56-62 (1978).
[CrossRef]

1977 (1)

R. P. Shrivastava and H. R. Zaidi, "Calculation of self-broadened widths of rotational Raman lines in H2 and N2," Can. J. Phys. 55, 542-548 (1977).
[CrossRef]

1976 (1)

1974 (1)

J. Bendtsen, "The rotational and rotation-vibrational Raman spectra of 14N2, 14N15N and 15N2," J. Raman Spectrosc. 2, 133-145 (1974).
[CrossRef]

1972 (1)

J. A. Cooney, "Measurements of atmospheric temperature profiles by Raman backscatter," J. Appl. Meteorol. 11, 108-112 (1972).
[CrossRef]

1971 (1)

G. Fiocco, G. Benedetti-Michelangeli, K. Maschberger, and E. Madonna, "Measurement of temperature and aerosol to molecule ratio in the troposphere by optical radar," Nature 229, 78-79 (1971).

1966 (1)

K. S. Jammu, G. E. St. John, and H. L. Welsh, "Pressure broadening of the rotational Raman lines of some simple gases," Can. J. Phys. 44, 797-814 (1966).
[CrossRef]

1953 (1)

L. B. Elterman, "Seasonal trends of temperature, density, and pressure to 67.6 km obtained with the searchlight probing technique," J. Geophys. Res. 58, 519-530 (1953).
[CrossRef]

1941 (1)

L. Henyey and J. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Aires, F.

F. Karbou, F. Aires, C. Prigent, and L. Eymard, "Potential of Advanced Microwave Sounding Unit-A (AMSU-A) and AMSU-B measurements for atmospheric temperature and humidity profiling over land," J. Geophys. Res. 110, D07109, doi: (2005).
[CrossRef]

Althausen, D.

I. Mattis, A. Ansmann, D. Althausen, V. Jaenisch, U. Wandinger, D. Müller, Y. F. Arshinov, S. M. Bobrovnikov, and I. B. Serikov, "Relative-humidity profiling in the troposphere with a Raman lidar," Appl. Opt. 41, 6451-6462 (2002).
[CrossRef] [PubMed]

S. Bobrovnikov, Y. F. Arshinov, I. B. Serikov, D. Althausen, A. Ansmann, I. Mattis, and U. Wandinger, "Daytime temperature profiling in the troposphere with a pure rotational Raman lidar," in Proceedings of the 21st International Laser Radar Conference, Part II (Defence R & D Canada, 2002), pp. 717-720.

Ansmann, A.

I. Mattis, A. Ansmann, D. Althausen, V. Jaenisch, U. Wandinger, D. Müller, Y. F. Arshinov, S. M. Bobrovnikov, and I. B. Serikov, "Relative-humidity profiling in the troposphere with a Raman lidar," Appl. Opt. 41, 6451-6462 (2002).
[CrossRef] [PubMed]

A. Ansmann, M. Riebesell, and C. Weitkamp, "Measurement of atmospheric aerosol extinction profiles with Raman lidar," Opt. Lett. 15, 746-748 (1990).
[CrossRef] [PubMed]

S. Bobrovnikov, Y. F. Arshinov, I. B. Serikov, D. Althausen, A. Ansmann, I. Mattis, and U. Wandinger, "Daytime temperature profiling in the troposphere with a pure rotational Raman lidar," in Proceedings of the 21st International Laser Radar Conference, Part II (Defence R & D Canada, 2002), pp. 717-720.

Arshinov, Y.

Arshinov, Y. F.

I. Mattis, A. Ansmann, D. Althausen, V. Jaenisch, U. Wandinger, D. Müller, Y. F. Arshinov, S. M. Bobrovnikov, and I. B. Serikov, "Relative-humidity profiling in the troposphere with a Raman lidar," Appl. Opt. 41, 6451-6462 (2002).
[CrossRef] [PubMed]

S. Bobrovnikov, Y. F. Arshinov, I. B. Serikov, D. Althausen, A. Ansmann, I. Mattis, and U. Wandinger, "Daytime temperature profiling in the troposphere with a pure rotational Raman lidar," in Proceedings of the 21st International Laser Radar Conference, Part II (Defence R & D Canada, 2002), pp. 717-720.

Assion, A.

G. Ehret, H. H. Klingenberg, U. Hefter, A. Assion, A. Fix, G. Proberaj, S. Berger, S. Geiger, and Q. Lü, "High peak and average power all solid-state laser systems for airborne LIDAR applications," LaserOpto 32, 29-37 (2000).

Barthès, J. C.

D. Morançais, F. Fabre, M. Schillinger, J. C. Barthès, M. Endemann, and A. Culoma, "ALADIN: the first European lidar in space," in Proceedings of the 22nd International Laser Radar Conference, ESA SP-561 (European Space Agency, 2004), Vol. 1, pp. 127-129.

Bauer, H.

V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
[CrossRef]

V. Wulfmeyer, H. Bauer, P. Di Girolamo, and C. Serio, "Comparison of active and passive remote sensing from space: an analysis based on the simulated performance of IASI and space borne differential absorption lidar," in Remote Sensing of Environment, (Elsevier, 2005), Vol. 95, pp. 211-230.
[CrossRef]

P. Di Girolamo, D. Summa, V. Wulfmeyer, H. Bauer, H. S. Bauer, A. Behrendt, M. Wirth, and B. Mayer, "Development of an end-to-end model to simulate the performances of a water vapour DIAL system in space," Final Report, ESA ESTEC Contract 16993/03/NL/FF (European Space Agency, 2004).

Bauer, H. S.

P. Di Girolamo, D. Summa, V. Wulfmeyer, H. Bauer, H. S. Bauer, A. Behrendt, M. Wirth, and B. Mayer, "Development of an end-to-end model to simulate the performances of a water vapour DIAL system in space," Final Report, ESA ESTEC Contract 16993/03/NL/FF (European Space Agency, 2004).

Baumgart, R.

Behrendt, A.

A. Behrendt, T. Nakamura, and T. Tsuda, "Combined temperature lidar for measurements in the troposphere, stratosphere, and mesosphere," Appl. Opt. 43, 2930-2939 (2004).
[CrossRef] [PubMed]

A. Behrendt, T. Nakamura, M. Onishi, R. Baumgart, and T. Tsuda, "Combined Raman lidar for the measurement of atmospheric temperature, water vapor, particle extinction coefficient, and particle backscatter coefficient," Appl. Opt. 41, 7657-7666 (2002).
[CrossRef]

A. Behrendt and J. Reichardt, "Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interference-filter-based polychromator," Appl. Opt. 39, 1372-1378 (2000).
[CrossRef]

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A. Behrendt, T. Nakamura, M. Onishi, R. Baumgart, and T. Tsuda, "Combined Raman lidar for the measurement of atmospheric temperature, water vapor, particle extinction coefficient, and particle backscatter coefficient," Appl. Opt. 41, 7657-7666 (2002).
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A. Behrendt, T. Nakamura, Y. Sawai, M. Onishi, and T. Tsuda, "Rotational vibrational-rotational Raman lidar: design and performance of the RASC Raman lidar at Shigaraki (34.8 deg N, 136.1 deg E), Japan," in Lidar Remote Sensing for Industry and Environment Monitoring II, U.N.Singh, ed., Proc. SPIE 4484, 151-162 (2001).

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M. Ostermeyer, P. Kappe, R. Menzel, and V. Wulfmeyer, "Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation system," Appl. Opt. 44, 582-590 (2005).
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M. Ostermeyer, P. Kappe, R. Menzel, and V. Wulfmeyer, "Frequency stabilized, diode pumped Nd:YAG laser with up to 0.5 J pulse energy and average output powers of 100W," in Proceedings of the 22nd International Laser Radar Conference, ESA SP-561 (European Space Agency, 2004), Vol. 1, pp. 57-60.

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O. Reitebuch, E. Chinal, Y. Durand, M. Endemann, R. Meynart, D. Morancais, and U. Paffrath, "Development of an airborne demonstrator for ADM-AEOLUS and campaign activities," in Proceedings of the 22nd International Laser Radar Conference, ESA SP-561 (European Space Agency, 2004), Vol. 1, pp. 1007-1010.

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V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
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W. F. Feltz, W. L. Smith, R. O. Knuteson, H. R. Revercomb, H. B. Howell, and H. H. Woolf, "Meteorological applications of temperature and water vapor retrievals from the ground-based Atmospheric Emitted Radiance Interferometer (AERI)," J. Appl. Meteorol. 37, 857-875 (1998).
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D. Morançais, F. Fabre, M. Schillinger, J. C. Barthès, M. Endemann, and A. Culoma, "ALADIN: the first European lidar in space," in Proceedings of the 22nd International Laser Radar Conference, ESA SP-561 (European Space Agency, 2004), Vol. 1, pp. 127-129.

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V. Wulfmeyer, H. Bauer, P. Di Girolamo, and C. Serio, "Comparison of active and passive remote sensing from space: an analysis based on the simulated performance of IASI and space borne differential absorption lidar," in Remote Sensing of Environment, (Elsevier, 2005), Vol. 95, pp. 211-230.
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Tsuda, T.

A. Behrendt, T. Nakamura, and T. Tsuda, "Combined temperature lidar for measurements in the troposphere, stratosphere, and mesosphere," Appl. Opt. 43, 2930-2939 (2004).
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Ullio, P.

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U. Wandinger, "Multiple-scattering influence on extinction and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars," Appl. Opt. 37, 417-427 (1998).
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Weitkamp, C.

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V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
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J. Buckley, T. Burnett, G. Sinnis, P. Coppi, P. Gondolo, J. Kapusta, J. McEnery, J. Norris, P. Ullio, and D. A. Williams, "Gamma-ray summary report," http://pancake.uchicago.edu/∼snowmass2001/p42.pdf (2002).

Wirth, M.

V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
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W. F. Feltz, W. L. Smith, R. O. Knuteson, H. R. Revercomb, H. B. Howell, and H. H. Woolf, "Meteorological applications of temperature and water vapor retrievals from the ground-based Atmospheric Emitted Radiance Interferometer (AERI)," J. Appl. Meteorol. 37, 857-875 (1998).
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Wulfmeyer, V.

M. Ostermeyer, P. Kappe, R. Menzel, and V. Wulfmeyer, "Diode-pumped Nd:YAG master oscillator power amplifier with high pulse energy, excellent beam quality, and frequency-stabilized master oscillator as a basis for a next-generation system," Appl. Opt. 44, 582-590 (2005).
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V. Wulfmeyer, H. Bauer, S. Crewell, G. Ehret, O. Reitebuch, C. Werner, M. Wirth, D. Engelbart, A. Rhodin, W. Wergen, A. Giesen, H. Grassl, G. Huber, H. Klingenberg, P. Mahnke, U. Kummer, C. Wührer, P. Ritter, R. Wallenstein, and U. Wandinger, "Lidar research network water vapour and wind," Meteorol. Z. 12, 6-24 (2003).
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V. Wulfmeyer, H. Bauer, P. Di Girolamo, and C. Serio, "Comparison of active and passive remote sensing from space: an analysis based on the simulated performance of IASI and space borne differential absorption lidar," in Remote Sensing of Environment, (Elsevier, 2005), Vol. 95, pp. 211-230.
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P. Di Girolamo, D. Summa, V. Wulfmeyer, H. Bauer, H. S. Bauer, A. Behrendt, M. Wirth, and B. Mayer, "Development of an end-to-end model to simulate the performances of a water vapour DIAL system in space," Final Report, ESA ESTEC Contract 16993/03/NL/FF (European Space Agency, 2004).

M. Ostermeyer, P. Kappe, R. Menzel, and V. Wulfmeyer, "Frequency stabilized, diode pumped Nd:YAG laser with up to 0.5 J pulse energy and average output powers of 100W," in Proceedings of the 22nd International Laser Radar Conference, ESA SP-561 (European Space Agency, 2004), Vol. 1, pp. 57-60.

A. Behrendt and V. Wulfmeyer, "Combining water vapor DIAL and rotational Raman temperature lidar for humidity, temperature, and particle measurements with high resolution and accuracy," in Lidar Remote Sensing for Industry and Environment Monitoring IV, U.N.Singh, ed., Proc. SPIE 5154, 61-64 (2003).

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U. Wandinger, "Multiple-scattering influence on extinction and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars," Appl. Opt. 37, 417-427 (1998).
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A. Behrendt, T. Nakamura, and T. Tsuda, "Combined temperature lidar for measurements in the troposphere, stratosphere, and mesosphere," Appl. Opt. 43, 2930-2939 (2004).
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Figures (17)

Fig. 1
Fig. 1

Calculated RR line signal intensities versus wavelength for N2 and O2 at 300 and 200 K, together with the transmission bands of the four RR channels.

Fig. 2
Fig. 2

Optical layout of the receiver. The receiver includes four interference filters (IF1–IF4). A Fabry–Perot interferometer (FPI1–FPI4) is used downstream for each IF for daytime measurements. A dichroic beam splitter (BS) separates the Stokes and anti-Stokes portions of the return signal. Low-J filters are located in an off-normal-incidence position to transmit RR lines with low J numbers and reflect those with high J numbers. PMTs, photomultiplier tubes; L1–L4, lenses.

Fig. 3
Fig. 3

Frequency shift of the center of each individual RR line from the center of the FPI peak profile (dashed curve). The figure also shows the frequency shift of the FWHM of the RR lines from the FPI transmission profile center (solid curves). Black curves are for the Stokes branch, while gray curves are for the anti-Stokes branch. The whole vertical scale represents the FPI profile width (0.2 cm−1) considered for the four FPIs.

Fig. 4
Fig. 4

FPI transmission factors versus height for the four FPIs.

Fig. 5
Fig. 5

Measurement sensitivity [(∂T/∂R)R]−1 as a function of temperature for both nighttime (IFs) and daytime (FPI + IFs) operation.

Fig. 6
Fig. 6

Daytime and nighttime performances in terms of measurement precision ΔT for clear-sky conditions (solid curves). Vertical profiles of pressure, temperature, and humidity are from U.S. Standard Atmosphere 1976; aerosol extinction is from the ESA ARMA median model; Sun zenith angle is equal to 75°; and surface albedo is equal to 0.35. The figure also illustrates daytime and nighttime measurement precision achieved with the anti-Stokes (AS) signals only (dashed curves). S, Stokes.

Fig. 7
Fig. 7

Daytime measurement precision ΔT in clear-sky conditions for different laser-pulse repetition frequencies in the range of 25–400 Hz. Average power is kept to 45 W.

Fig. 8
Fig. 8

Measurement precision ΔT in cloud-free conditions for the tropical, the sub-Arctic winter, and the U.S. Standard atmospheres.

Fig. 9
Fig. 9

Temperature profiles of the tropical, the sub-Arctic winter, and the U.S. Standard (1976) atmospheres.

Fig. 10
Fig. 10

Daytime measurement precision ΔT for different Sun zenith angles (60°, 75°, 80°, and 85°). S, Stokes; AS, anti-Stokes.

Fig. 11
Fig. 11

Daytime measurement precision ΔT for different surface albedos (0.1, 0.35, 0.7, and 0.95). S, Stokes; AS, anti-Stokes.

Fig. 12
Fig. 12

Particle backscatter profile including an aerosol component from the ESA median model and two cloud layers: an altostratus located at 3 km, with a vertical extent of 180 m and an optical thickness of 0.3, and a cirrus located at 9 km, with a vertical extent of 180 m and an optical thickness of 0.3.

Fig. 13
Fig. 13

Daytime and nighttime measurement precision in the presence of clouds. Three different optical thickness values are considered for the cirrus cloud: 0.3, 0.65, and 1.3 (for the latter two cases, performances are illustrated only for nighttime operation).

Fig. 14
Fig. 14

RH measurement precision for daytime operation (bold curve), together with the different contributions, one associated with temperature measurement precision (dashed curve) and one associated with water-vapor number density measurement precision (thin curve).

Fig. 15
Fig. 15

Performance of particle extinction coefficient profiling: vertical profile of Δαaer(z)∕αaer(z) for daytime (gray curve) and nighttime (black curve) operation, together with the vertical profile of aerosol extinction of the ESA median model (dashed curve). In the presence of clouds or thicker aerosol layers, performances for extinction measurements are expected to be noticeably better.

Fig. 16
Fig. 16

Nighttime measurement precision ΔT in cloud-free conditions for different values of the average power of the lidar transmitter (45, 100, 200, 400 W). S, Stokes; AS, anti-Stokes.

Fig. 17
Fig. 17

Same as Fig. 16 but for daytime. S, Stokes; AS, anti-Stokes.

Tables (4)

Tables Icon

Table 1 Observational Target/Threshold Requirements to be Fulfilled by Networks of Satellite Remote Sensors a

Tables Icon

Table 2 Main System Components and Their Specifications

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Table 3 Specifications of the Four Interference Filters Used in the Simulations

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Table 4 Specifications of the Four FPIs Considered for Daytime Simulations

Equations (25)

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R ( T ) = P hi J S ( z [ T ] ) + P hi J AS ( z [ T ] ) P lo J S ( z [ T ] ) + P lo J AS ( z [ T ] ) exp ( α / T + β ) ,
P lo J / hi J S / AS ( z ) = λ 0 P 0 hc A z 2 η Δ t τ 0 ( z ) τ lo J / hi J S / AS ( z ) × i = O 2 , N 2 J i N i ( z ) τ RR ( J i ) F J i ( T ) ( d σ J i d Ω ) π ,
Δ T ( z ) = T ( z ) R R ( z ) P lo J S ( z ) + b lo J S [ P lo J S ( z ) ] 2 + P hi J S ( z ) + b hi J S [ P hi J S ( z ) ] 2 + P lo J AS ( z ) + b lo J AS [ P lo J AS ( z ) ] 2 + P hi J AS ( z ) + b hi J AS [ P hi J AS ( z ) ] 2 .
b ( λ ) = b atm ( λ ) + b surf ( λ ) + b cloud ( λ ) .
b atm ( λ ) = S 0 A π FOV 2 0 TOA exp { z TOA α atm ( λ , z ) d z } exp { z TOA α atm ( λ , z ) cos Θ  d z } [ β mol ( λ , z ) 1 + cos 2 Θ 2 + β par ( λ , z ) P HG ( Θ ) P HG ( 0 ) ] d z ,
b surf ( λ ) = S 0 cos Θ A FOV 2 R surf exp { 0 TOA α atm ( λ , z ) d z } exp { 0 TOA α atm ( λ , z ) cos Θ   d z } ,
b cloud ( ν ˜ , r ) = S 0 cos Θ A FOV 2 R cloud ( τ , Θ ) exp { z cloud TOA α atm ( λ , z ) d z } exp { z cloud TOA α atm ( λ , z ) cos Θ  d z } ,
P HG ( Θ ) = 1 2 1 g 2 ( 1 + 2 g cos Θ + g 2 ) 1.5 ,
Δ T ( P 0 AηΔxΔ z ) 1 / 2 ,
Δ ν c ( J ) = Δ ν sep ( J ) Δ ν sep ( J ) FSR [ J J ] 1 J max J min J = J min J max [ Δ ν sep ( J ) Δ ν sep ( J ) FSR [ J J ] ] ,
T pk = ( 1 a 1 R* ) 2 f f R ,
T T T = 100 × α ln R β α ln ( R + Δ R ) β α ln R β = 100 × [ 1 ln R β ln ( R + Δ R ) β ] .
T T T = 100 × Δ R R ( ln R β ) .
RH ( z ) = e ( z ) e S ( z ) ,
e ( z ) = n H 2 O ( z ) k T ( z ) ,
e S ( z ) = c exp [ a ( T 273.15 ) T 273.15 + b ] ,
RH ( z ) = n H 2 O ( z ) k T ( z ) c exp [ a ( T 273.15 ) T 273.15 + b ] .
Δ RH ( z ) = ( RH n H 2 O ) 2 Δ n H 2 O               2 ( z ) + ( RH T ) 2 Δ T 2 ( z ) .
Δ RH ( z ) RH ( z ) = 100 × Δ n H 2 O                 2 ( z ) n H 2 O                 2 ( z ) + ( 1 a b T [ T 273.15 + b ] 2 ) 2 Δ T 2 ( z ) T 2 ( z ) .
P ref           S ( z ) = P lo J           S ( z ) + c S P hi J           S ( z ) for   the   Stokes   branch ,
P re f           AS ( z ) = P lo J           AS ( z ) + c AS P hi J           AS ( z ) for   the   anti-Stokes   branch .
α aer ( z ) = 1 2 d d z ln { N ( z ) [ P ref           S ( z ) + P ref         AS ( z ) ] z 2 } α mol ( z ) ,
Δ α aer ( z ) = 1 2 Δ z [ ( Δ P ref         S ) 2 + ( Δ P ref       AS ) 2 P ref           S + P ref         AS ] ,
Δ α aer ( z ) α aer ( z ) = 100 2 Δ τ aer [ ( Δ P ref S ) 2 + ( Δ P ref AS ) 2 P ref S + P ref AS ] ,
Δ α aer ( z ) α aer ( z ) = 100 2 Δ τ aer [ ( P ref S + bk ref S ) ( P ref S + P ref AS ) 2 + ( P ref AS + bk ref AS ) ( P ref S + P ref AS ) 2 ] .

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