Abstract

We demonstrate the feasibility of retrieval of temperature and pressure profiles from spaceborne limb-sounding spectroscopic measurements in the submillimetric region. Whether these profiles can be retrieved determines whether a submillimetric instrument can be self-sufficient as far as the atmospheric model is concerned or whether complementary sensors in other spectral regions, dedicated to temperature and pressure measurements, are needed. Molecular-oxygen transitions are selected for the purpose of temperature and pressure retrieval on the basis of realistic observational parameters. We use a mathematical model of the retrieval process to evaluate the information content of the spectral features and to study the trade-off between the uncertainty of the retrieved profiles and their vertical resolution. It is shown that, using only one oxygen transition and without any constraint, one can achieve uncertainties of 5% for both temperature and pressure from 10 to ∼40 km of altitude with a vertical resolution of 3 km; above 40 km the vertical resolution needs to be degraded to limit the uncertainties. The possibility of exploiting a priori information is discussed, as well as the effects of external constraints that can be used to improve the quality of the retrieved profiles. The sources of systematic error that need to be considered for the compilation of the total error budget are also evaluated.

© 1999 Optical Society of America

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References

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  1. S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).
  2. M. Carlotti, “Global fit approach to the analysis of limb-scanning atmospheric measurements,” Appl. Opt. 27, 3250–3254 (1988).
    [CrossRef] [PubMed]
  3. M. Carlotti, B. Carli, “Approach to the design and data analysis of a limb-scanning experiment,” Appl. Opt. 33, 3237–3249 (1994).
    [CrossRef] [PubMed]
  4. R. E. Kalman, “Algebraic aspects of the generalized inverse of a rectangular matrix,” in Proceedings of the Advanced Seminar on Generalized Inverse and Applications, M. Z. Nashed, ed. (Academic, San Diego, Calif., 1976), pp. 111–124.
  5. L. S. Rothman, R. R. Gamache, A. Goldman, L. R. Brown, R. A. Toth, H. M. Pickett, R. L. Poynter, J.-M. Flaud, C. Camy-Peyret, A. Barbe, N. Husson, C. P. Rinsland, M. A. H. Smith, “HITRAN database: 1986 edition,” Appl. Opt. 26, 4058–4097 (1987).
    [CrossRef] [PubMed]
  6. C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
    [CrossRef]
  7. J. W. Waters, “Microwave limb-sounding of Earth’s upper atmosphere,” Atmos. Res. 23, 391–410 (1989).
    [CrossRef]

1994 (1)

1989 (1)

J. W. Waters, “Microwave limb-sounding of Earth’s upper atmosphere,” Atmos. Res. 23, 391–410 (1989).
[CrossRef]

1988 (1)

1987 (1)

1976 (1)

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
[CrossRef]

Arzner, K.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Barbe, A.

Brown, L. R.

Buehler, S.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Camy-Peyret, C.

Carli, B.

Carlotti, M.

Flaud, J.-M.

Gamache, R. R.

Goldman, A.

Husson, N.

Kalman, R. E.

R. E. Kalman, “Algebraic aspects of the generalized inverse of a rectangular matrix,” in Proceedings of the Advanced Seminar on Generalized Inverse and Applications, M. Z. Nashed, ed. (Academic, San Diego, Calif., 1976), pp. 111–124.

Kerridge, B. J.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Kuenzi, K.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Peter, R.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Pickett, H. M.

Poynter, R. L.

Reburn, W. J.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Rinsland, C. P.

Rodgers, C. D.

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
[CrossRef]

Rothman, L. S.

Siddans, R.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Sinnhuber, B. M.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Smith, M. A. H.

Toth, R. A.

Urban, J.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

von Engeln, A.

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

Waters, J. W.

J. W. Waters, “Microwave limb-sounding of Earth’s upper atmosphere,” Atmos. Res. 23, 391–410 (1989).
[CrossRef]

Appl. Opt. (3)

Atmos. Res. (1)

J. W. Waters, “Microwave limb-sounding of Earth’s upper atmosphere,” Atmos. Res. 23, 391–410 (1989).
[CrossRef]

Rev. Geophys. Space Phys. (1)

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
[CrossRef]

Other (2)

S. Buehler, A. von Engeln, K. Kuenzi, B. M. Sinnhuber, J. Urban, R. Siddans, B. J. Kerridge, W. J. Reburn, R. Peter, K. Arzner, “The retrieval of data from sub-millimeter limb sounding,” (30September1998).

R. E. Kalman, “Algebraic aspects of the generalized inverse of a rectangular matrix,” in Proceedings of the Advanced Seminar on Generalized Inverse and Applications, M. Z. Nashed, ed. (Academic, San Diego, Calif., 1976), pp. 111–124.

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Figures (14)

Fig. 1
Fig. 1

Simulation of three atmospheric spectral features for the 16O18O transition at 731.2 GHz. Observations are simulated with (a) 15-km, (b) 35-km, and (c) 55-km tangent altitude (T.H.). Solid curves, simulations include all the transitions of the spectroscopic database. (a) The dashed curve refers to simulation without the oxygen transition; (b), (c) the dashed curves overlap the frequency axis.

Fig. 2
Fig. 2

Sensitivity functions for observations with infinitesimal spectral resolution and field of view. Three sample frequencies are shown, defined by their displacement (Δ) from the central frequency of the transition.

Fig. 3
Fig. 3

Sensitivity functions for observations with 3-MHz spectral resolution and infinitesimal field of view at the same sample frequencies of Fig. 2.

Fig. 4
Fig. 4

Sensitivity functions for observations with 3-MHz spectral resolution and 1-mrad conic field of view at the same sample frequencies of Fig. 2.

Fig. 5
Fig. 5

Example of three vectors that make a base for the layer-model space defined by the four altitudes h 1, h 2, h 3, and h 4.

Fig. 6
Fig. 6

Percent-error values (solid curve) and vertical resolution (dashed curve) for the temperature profile retrieved with 3-km constant vertical resolution.

Fig. 7
Fig. 7

Percent-error values (solid curve) and vertical resolution (dashed curve) for the temperature profile retrieved with the goal of limiting errors below 5%.

Fig. 8
Fig. 8

Percent-error values (solid curve) and vertical resolution (dashed curve) for the temperature profile when it is retrieved simultaneously with the pressure profile.

Fig. 9
Fig. 9

Percent-error values (solid curve) and vertical resolution (dashed curve) for the pressure profile when it is retrieved simultaneously with the temperature profile.

Fig. 10
Fig. 10

Percent-error values (solid curve) and vertical resolution (dashed curve) for the temperature profile when it is retrieved simultaneously with the pressure profile. The two profile segmentations have minimum overlap of the layers used for temperature and pressure.

Fig. 11
Fig. 11

Percent-error values (solid curve) and vertical resolution (dashed curve) for the pressure profile when it is retrieved simultaneously with the temperature profile. The two profile segmentations have minimum overlap of the layers used for temperature and pressure.

Fig. 12
Fig. 12

Percent-error values (solid curve) and vertical resolution (dashed curve) for the temperature profile when hydrostatic equilibrium conditions are assumed.

Fig. 13
Fig. 13

Combination of the retrieval errors with the errors of a priori information for 3-km constant vertical resolution. Solid curves, retrieval errors; short dashed–long-dashed curves, errors of case (1) a priori information; dotted–dashed curves, errors of case (2) a priori information; long-dashed curves, combined errors for case (1); short-dashed curves, combined errors for case (2).

Fig. 14
Fig. 14

Reduction of the errors owing to hydrostatic equilibrium constraint in the case of 3-km constant vertical resolution. Solid curves, retrieval errors; long-dashed curves, errors in the case of constraint with 50% correlation between 0.5-km tangent-altitude uncertainties; short-dashed curves, errors in the case of constraint with 85% correlation between 0.5-km tangent-altitude uncertainties.

Tables (1)

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Table 1 Instrumental Parameters

Equations (19)

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Nx=0 Kx, zyzdz,
Kx, z=Sx, qzlnqzq˜z,
yz=lnqz-lnq˜z.
n=Ky,
yˆ=Dn.
D=HTHKTS-1KHT-1HKTS-1,
V=DSDT,
cov yˆ=σ2DDT.
pn=p0 exp-MR g i=0n1Ti Δzi,
Kν=-+ KνIν-νdν-+ Iν-νdν,
Kθ=-π/2+π/2 KθAθ-θdθ-π/2+π/2 Aθ-θdθ,
yt=V-1+V1-1-1V-1y+V1-1y1,
Vt=V-1+V1-1-1.
Δz1=z2-z1...ΔzNSC-1=zNSC-zNSC-1,
Δzi=RMg Ti lnpipi+1.
Δz=K1y,
yˆ1=D1Δz.
D1=HTHK1TSZ-1K1HT-1HK1TSZ-1,
V1=D1SzD1T.

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