Abstract

A simple and computationally efficient model is developed for calculation of slant path atmospheric transmittances in the microwave and millimeter spectral regions. The model deals simultaneously with absorption by oxygen and water vapor. Its accuracy is assessed for a range of atmospheric conditions for spectral intervals corresponding to the channels of the Advanced Microwave Sounding Unit. The model is found to be very accurate (≤0.001 error in transmittance) where water vapor absorption is weak. It is less accurate (~0.02 error in transmittance) at frequencies of strong water vapor absorption but should be adequate for most tropospheric sounding applications.

© 1988 Optical Society of America

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References

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  1. W. L. Smith, H. M. Woolf, A. J. Schreiner, “Simultaneous Retrieval of Surface and Atmospheric Parameters: A Physical and Analytically Direct Approach,” in Advances in Remote Sensing (A. Deepak Publishing, Hampton, VA, 1985), pp. 221–230.
  2. J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
    [CrossRef]
  3. L. M. McMillin, H. E. Fleming, “Atmospheric Transmittance of an Absorbing Gas: a Computationally Fast and Accurate Transmittance Model for Absorbing Gases with Constant Mixing Ratios in Inhomogeneous Atmospheres,” Appl. Opt. 15, 358 (1976).
    [CrossRef] [PubMed]
  4. L. M. McMillin, H. E. Fleming, A. Arking, D. Chesters, “Accuracies of Three Computationally Efficient Algorithms for Computing Atmospheric Transmittances,” Appl. Opt. 19, 2267 (1980).
    [CrossRef] [PubMed]
  5. H. E. Fleming, L. M. McMillin, “Atmospheric Transmittance of an Absorbing Gas. 2: A Computationally Fast and Accurate Transmittance Model for Slant Paths at Different Zenith Angles,” Appl. Opt. 16, 1366 (1977).
    [CrossRef] [PubMed]
  6. L. M. McMillin, H. E. Fleming, M. L. Hill, “Atmospheric Transmittance of an Absorbing Gas. 3: A Computationally Fast and Accurate Transmittance Model for Absorbing Gases with Variable Mixing Ratios,” Appl. Opt. 18, 1600 (1979).
    [CrossRef] [PubMed]
  7. J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
    [CrossRef]
  8. D. R. Pick, “Operational Sounding of the Lower Atmosphere Using Millimetre Waves,” in Proceedings, Sixteenth European Microwave Conference, Dublin (1986), pp. 31–41.
  9. P. W. Rosenkranz, “Shape of the 5mm Oxygen Band in the Atmosphere,” IEEE Trans. Antennas Propag. AP-23, 498 (1975).
    [CrossRef]
  10. H. J. Liebe, “Modelling Attenuation and Phase of Radio Waves in Air at Frequencies Below 1000 GHz,” Radio Sci. 16, 1183 (1981).
    [CrossRef]
  11. A. H. Barrett, V. K. Chung, “A Method for the Determination of High-Altitude Water Vapor Abundance from Ground-Based Microwave Observations,” J. Geophys. Res. 67, 4259 (1962).
    [CrossRef]
  12. M. P. Weinreb, A. C. Neuendorffer, “Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres,” J. Atmos. Sci. 30, 662 (1973).
    [CrossRef]
  13. J. R. Eyre, “Inversion of Cloudy Satellite Sounding Radiances by Non-linear Optimal Estimation: Theory and Simulation for TOVS,” submitted to Q.J.R. Meteorol. Soc. (1987).

1984

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

1983

J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
[CrossRef]

1981

H. J. Liebe, “Modelling Attenuation and Phase of Radio Waves in Air at Frequencies Below 1000 GHz,” Radio Sci. 16, 1183 (1981).
[CrossRef]

1980

1979

1977

1976

1975

P. W. Rosenkranz, “Shape of the 5mm Oxygen Band in the Atmosphere,” IEEE Trans. Antennas Propag. AP-23, 498 (1975).
[CrossRef]

1973

M. P. Weinreb, A. C. Neuendorffer, “Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres,” J. Atmos. Sci. 30, 662 (1973).
[CrossRef]

1962

A. H. Barrett, V. K. Chung, “A Method for the Determination of High-Altitude Water Vapor Abundance from Ground-Based Microwave Observations,” J. Geophys. Res. 67, 4259 (1962).
[CrossRef]

Arking, A.

Barrett, A. H.

A. H. Barrett, V. K. Chung, “A Method for the Determination of High-Altitude Water Vapor Abundance from Ground-Based Microwave Observations,” J. Geophys. Res. 67, 4259 (1962).
[CrossRef]

Chahine, M. T.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

Chesters, D.

Chung, V. K.

A. H. Barrett, V. K. Chung, “A Method for the Determination of High-Altitude Water Vapor Abundance from Ground-Based Microwave Observations,” J. Geophys. Res. 67, 4259 (1962).
[CrossRef]

Eyre, J. R.

J. R. Eyre, “Inversion of Cloudy Satellite Sounding Radiances by Non-linear Optimal Estimation: Theory and Simulation for TOVS,” submitted to Q.J.R. Meteorol. Soc. (1987).

Fleming, H. E.

Hill, M. L.

Liebe, H. J.

H. J. Liebe, “Modelling Attenuation and Phase of Radio Waves in Air at Frequencies Below 1000 GHz,” Radio Sci. 16, 1183 (1981).
[CrossRef]

McMillin, L. M.

Neuendorffer, A. C.

M. P. Weinreb, A. C. Neuendorffer, “Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres,” J. Atmos. Sci. 30, 662 (1973).
[CrossRef]

Pick, D. R.

D. R. Pick, “Operational Sounding of the Lower Atmosphere Using Millimetre Waves,” in Proceedings, Sixteenth European Microwave Conference, Dublin (1986), pp. 31–41.

Reuter, D.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
[CrossRef]

Rosenfield, J.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
[CrossRef]

Rosenkranz, P. W.

P. W. Rosenkranz, “Shape of the 5mm Oxygen Band in the Atmosphere,” IEEE Trans. Antennas Propag. AP-23, 498 (1975).
[CrossRef]

Schreiner, A. J.

W. L. Smith, H. M. Woolf, A. J. Schreiner, “Simultaneous Retrieval of Surface and Atmospheric Parameters: A Physical and Analytically Direct Approach,” in Advances in Remote Sensing (A. Deepak Publishing, Hampton, VA, 1985), pp. 221–230.

Smith, W. L.

W. L. Smith, H. M. Woolf, A. J. Schreiner, “Simultaneous Retrieval of Surface and Atmospheric Parameters: A Physical and Analytically Direct Approach,” in Advances in Remote Sensing (A. Deepak Publishing, Hampton, VA, 1985), pp. 221–230.

Susskind, J.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
[CrossRef]

Weinreb, M. P.

M. P. Weinreb, A. C. Neuendorffer, “Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres,” J. Atmos. Sci. 30, 662 (1973).
[CrossRef]

Woolf, H. M.

W. L. Smith, H. M. Woolf, A. J. Schreiner, “Simultaneous Retrieval of Surface and Atmospheric Parameters: A Physical and Analytically Direct Approach,” in Advances in Remote Sensing (A. Deepak Publishing, Hampton, VA, 1985), pp. 221–230.

Appl. Opt.

IEEE Trans. Antennas Propag.

P. W. Rosenkranz, “Shape of the 5mm Oxygen Band in the Atmosphere,” IEEE Trans. Antennas Propag. AP-23, 498 (1975).
[CrossRef]

J. Atmos. Sci.

M. P. Weinreb, A. C. Neuendorffer, “Method to Apply Homogeneous-Path Transmittance Models to Inhomogeneous Atmospheres,” J. Atmos. Sci. 30, 662 (1973).
[CrossRef]

J. Geophys. Res.

A. H. Barrett, V. K. Chung, “A Method for the Determination of High-Altitude Water Vapor Abundance from Ground-Based Microwave Observations,” J. Geophys. Res. 67, 4259 (1962).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote Sensing of Weather and Climate Parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677 (1984).
[CrossRef]

J. Susskind, J. Rosenfield, D. Reuter, “An Accurate Radiative Transfer Model for use in the Direct Physical Inversion of HIRS2 and MSU Temperature Sounding Data,” J. Geophys. Res. 88, 8550 (1983).
[CrossRef]

Radio Sci.

H. J. Liebe, “Modelling Attenuation and Phase of Radio Waves in Air at Frequencies Below 1000 GHz,” Radio Sci. 16, 1183 (1981).
[CrossRef]

Other

D. R. Pick, “Operational Sounding of the Lower Atmosphere Using Millimetre Waves,” in Proceedings, Sixteenth European Microwave Conference, Dublin (1986), pp. 31–41.

W. L. Smith, H. M. Woolf, A. J. Schreiner, “Simultaneous Retrieval of Surface and Atmospheric Parameters: A Physical and Analytically Direct Approach,” in Advances in Remote Sensing (A. Deepak Publishing, Hampton, VA, 1985), pp. 221–230.

J. R. Eyre, “Inversion of Cloudy Satellite Sounding Radiances by Non-linear Optimal Estimation: Theory and Simulation for TOVS,” submitted to Q.J.R. Meteorol. Soc. (1987).

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Figures (3)

Fig. 1
Fig. 1

Root-mean-square errors in transmittance at the pressure level of maximum error for each channel for the dependent profile set (+) and for three independent sets (——, mid-latitude; — — —, high latitude; - - - - -, low latitude). Values are averages over all zenith angles.

Fig. 2
Fig. 2

As in Fig. 1, except averages are for nadir calculations only.

Fig. 3
Fig. 3

Root-mean-square errors in transmittance at the pressure levels of maximum errors for the dependent profile set at nadir. Lines are for the algorithm of Eq. (13) with different values of N. Crosses are for the algorithm of Eq. (15).

Tables (1)

Tables Icon

Table I AMSU Spectral Characteristics

Equations (16)

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τ i Θ = exp ( - ( sec Θ / g ) 0 p i { k o ( T ( p ) , p ) c o ( p ) + k w [ T ( p ) , p , c w ( p ) ] c w ( p ) } d p ) ,
τ i Θ = exp { - ( sec Θ / g ) j = 1 i [ k o ( T j , p j ) c j o + k w ( T j , p j , c j w ) c j w ] Δ p j ] } ,
ln ( τ i Θ / τ i - 1 Θ ) = - ( sec Θ / g ) Δ p i [ k o ( T i , p i ) c i o + k w ( T i , p i , c i w ) c i w ] .
δ ln ( τ i Θ / τ i - 1 Θ ) = ( sec Θ / g ) Δ p i ( c i o d k i o d T i δ T i + c i w d k i w d T i δ T i + c i w d k i w d c i w δ c i w + k i w δ c i w ) .
δ ln ( τ i Θ / τ i - 1 Θ ) sec Θ ( α 1 i δ T i + α 2 i c i δ T i + α 3 i δ c i + α 4 i c i δ c i ) ,
δ c i δ T i = c i δ T i - c ¯ i δ T i ,
δ c i 2 = c i δ c i - c ¯ i δ c i ,
δ ln ( τ i Θ / τ i - 1 Θ ) sec Θ ( β 1 i δ T i + β 2 i δ c i δ T i + β 3 i δ c i + β 4 i δ c i 2 ) ,
ln ( τ i Θ / τ i - 1 Θ ) = sec Θ j = 1 10 a j i X j i ,
X 1 i = δ T i ,             X 2 i = δ T i 2 ,             X 3 i = k = 1 i δ T k Δ p k / p i , X 4 i = 2 k = 1 i δ T k p k Δ p k / p i 2 ,             X 5 i = δ c i ,             X 6 i = δ c i 2 , X 7 i = k = 1 i δ c k Δ p k / p i ,             X 8 i = 2 k = 1 i δ c k p k Δ p k / p i 2 , X 9 i = δ c i δ T i ,             X 10 i = 1.
ln ( τ i Θ / τ i - 1 Θ ) - sec Θ j = 1 10 a j i X j i = ( sec Θ - 1 ) j = 1 4 b j i Y j i ,
τ i Θ = τ i - 1 Θ exp ( Z ) ,
Z = sec Θ j = 1 10 a j i X j i + ( sec Θ - 1 ) j = 1 4 b j i Y j i .
τ i Θ = τ i - 1 Θ n = 0 N Z n n ! .
τ i Θ / τ i - 1 Θ = sec Θ j = 1 10 a j i X j i
τ i Θ = τ i - 1 Θ Z ,

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