Abstract

In this study a ray-tracing model that uses atmospheric data from VIZ and Vaisala RS80 rawinsondes is compared with the observed astronomical refraction presented by the setting Sun as seen from Stony Plain, Alberta, Canada. Photogrammetric measurements taken from photographs of the setting Sun show good agreement with the model for the 14 and 22 December 1998 sunsets. The poorer model results for the 8 December sunset appear to be caused by an obsolete and possibly defective VIZ rawinsonde. The results suggest that the ray-tracing model can produce improved refraction values when compared with the Pulkovo tables [Pulkovo Observatory, Refraction Tables of the Pulkovo Observatory, 5th ed. (Nauka, Leningrad, 1985)]. However, they also indicate that the inverse solution (i.e., extracting the temperature profile from refraction measurements) may produce no improvement on U.S. Standard Atmosphere adjusted to the surface conditions.

© 2003 Optical Society of America

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References

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  1. G. M. Clemence, “Astronomical refraction at great zenith angles,” Astron. J. 56, 123–124 (1951).
    [CrossRef]
  2. Pulkovo Observatory, Refraction Tables of the Pulkovo Observatory, 5th ed. (Nauka, Leningrad, 1985).
  3. “Vaisala product specifications” Vaisala Oyj, Helsinki, Finland, 1998, http://www.vaisala.fi .
  4. J. Meeus, Astronomical Formulae for Calculators (Willmann-Bell, Richmond, Va., 1988).
  5. R. D. Sampson, “A comparison of photogrammetrically determined astronomical refraction of sunlight at high zenith angles with a ray-tracing computer model employing rawinsonde profiles,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 2000).
  6. D. Bruton, “Optical determination of atmospheric temperature profiles,” Ph.D. dissertation (Texas AM University, College Station, Texas, 1996).
  7. J. M. Wallace, P. V. Hobbs, Atmospheric Science (Academic, London, 1977).
  8. J. V. Iribarne, W. L. Godson, Atmospheric Thermodynamics (Reidel, Dordrecht, The Netherlands, 1981).
    [CrossRef]
  9. P. E. Ciddor, “Refractive index of air: new equations for the visible and infrared,” Appl. Opt. 35, 1566–1573 (1996).
    [CrossRef] [PubMed]
  10. R. Sampson, “Atmospheric refraction and sunrise and sunset,” Sky Telesc. 85, 96–97 (1993).
  11. A. B. Fraser, “The green flash and clear air turbulence,” Atmos. 13, 1–10 (1975).
  12. W. H. Lehn, “The Novaya Zemlya effect: an arctic mirage,” J. Opt. Soc. Am. 69, 776–781 (1979).
    [CrossRef]
  13. M. Minnaert, Light and Color in the Outdoors (Springer-Verlag, New York, 1993).
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    [CrossRef] [PubMed]
  16. S. P. Arya, Introduction to Micrometeorology (Academic, London, 1988).
  17. R. B. Stull, Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
    [CrossRef]
  18. P. R. Wolf, B. A. Dewitt, Elements of Photogrammetry (McGraw-Hill, Boston, 2000).
  19. R. D. Sampson, A. E. Peterson, E. P. Lozowski, “Photogrammetric calibration of a consumer grade flatbed scanner,” Geomatica (to be published).
  20. T. R. Oke, Boundary Layer Climates (Methuen, London, 1987).
  21. A. A. Thom, “An empirical investigation of atmospheric refraction,” Emp. Surv. Rev. 14, 248–262 (1958).
    [CrossRef]
  22. G. Bomford, Geodesy, 4th ed. (Clarendon, Oxford, UK, 1980).
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  24. R. D. Sampson, “Atmospheric refraction and its effects on sunrise and sunset,” M.S. thesis (University of Alberta, Edmonton, Alberta, Canada, 1994).
  25. “Scion image for windows,” Scion Corporation, Frederick, Md., 1999, http://www.scioncorp.com/index.htm .
  26. J. C. McGlone, “Analytic data-reduction schemes in non-topographic photogrammetry,” in Non-Topographic Photogrammetry, 2nd ed., H. M. Karara, ed. (American Society for Photogrammetry and Remote Sensing, Washington, D.C., 1989).
  27. W. H. Press, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, UK, 1992).
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    [CrossRef]
  29. D. Carlsen, Winnipeg Office of Meteorological Services of Canada, Environment Canada, Winnipeg, Manitoba, Canada (personal communication, 2000).
  30. “Mark II microsonde,” Sippican Inc., Marion, Mass., 1998, http://www.sippican.com/pdf/mark2.pdf .
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    [CrossRef]
  33. A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
    [CrossRef]
  34. V. Antikainen, V. Hyvönen, “The accuracy of Vaisala RS 80 radiosonde,” in Proceedings of the Fifth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1983), pp. 134–140.
  35. A. I. Mahan, “Astronomical refraction—some history and theories,” Appl. Opt. 1, 497–511 (1962).
    [CrossRef]
  36. J. R. Taylor, An Introduction to Error Analysis (University Science, Mill Valley, Calif., 1982).
  37. M. G. Green, Spherical Astronomy (Cambridge U. Press, Cambridge, UK, 1985).
  38. U.S. Standard Atmosphere (U.S. Government Printing Office, Washington, D.C., 1976).
  39. A. Paukkenen, Vaisala Oyj, Helsinki, Finland, ari.paukkunen@vaisala.com (personal communications, 2000).

1998 (1)

T. K. Flesch, J. D. Wilson, “Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics,” Agri. For. Meteorol. 93, 243–258 (1998).
[CrossRef]

1997 (2)

A. T. Young, G. W. Kattawar, P. Parviainen, “Sunset science. I. The mock mirage,” Appl. Opt. 36, 2689–2700 (1997).
[CrossRef] [PubMed]

A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
[CrossRef]

1996 (1)

1993 (1)

R. Sampson, “Atmospheric refraction and sunrise and sunset,” Sky Telesc. 85, 96–97 (1993).

1991 (1)

B. E. Schwartz, C. A. Doswell, “North American rawinsonde observations: problems, concerns, and a call to action,” Bull. Am. Meteorol. Soc. 72, 1885–1896 (1991).
[CrossRef]

1979 (1)

1975 (1)

A. B. Fraser, “The green flash and clear air turbulence,” Atmos. 13, 1–10 (1975).

1962 (1)

1958 (1)

A. A. Thom, “An empirical investigation of atmospheric refraction,” Emp. Surv. Rev. 14, 248–262 (1958).
[CrossRef]

1951 (1)

G. M. Clemence, “Astronomical refraction at great zenith angles,” Astron. J. 56, 123–124 (1951).
[CrossRef]

Antikainen, V.

V. Antikainen, V. Hyvönen, “The accuracy of Vaisala RS 80 radiosonde,” in Proceedings of the Fifth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1983), pp. 134–140.

Arya, S. P.

S. P. Arya, Introduction to Micrometeorology (Academic, London, 1988).

Bomford, G.

G. Bomford, Geodesy, 4th ed. (Clarendon, Oxford, UK, 1980).

Brinker, R. C.

R. C. Brinker, P. R. Wolf, Elementary Surveying (Harper Row, New York, 1984).

Bruton, D.

D. Bruton, “Optical determination of atmospheric temperature profiles,” Ph.D. dissertation (Texas AM University, College Station, Texas, 1996).

Carlsen, D.

D. Carlsen, Winnipeg Office of Meteorological Services of Canada, Environment Canada, Winnipeg, Manitoba, Canada (personal communication, 2000).

Ciddor, P. E.

Clemence, G. M.

G. M. Clemence, “Astronomical refraction at great zenith angles,” Astron. J. 56, 123–124 (1951).
[CrossRef]

Dewitt, B. A.

P. R. Wolf, B. A. Dewitt, Elements of Photogrammetry (McGraw-Hill, Boston, 2000).

Doswell, C. A.

B. E. Schwartz, C. A. Doswell, “North American rawinsonde observations: problems, concerns, and a call to action,” Bull. Am. Meteorol. Soc. 72, 1885–1896 (1991).
[CrossRef]

Finger, F. G.

F. J. Schmidlin, F. G. Finger, “Conclusions and recommendations resulting from the WMO international radiosonde intercomparison,” in Proceedings of the Sixth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1987), pp. 459–462.

Flesch, T. K.

T. K. Flesch, J. D. Wilson, “Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics,” Agri. For. Meteorol. 93, 243–258 (1998).
[CrossRef]

Fraser, A. B.

A. B. Fraser, “The green flash and clear air turbulence,” Atmos. 13, 1–10 (1975).

Godson, W. L.

J. V. Iribarne, W. L. Godson, Atmospheric Thermodynamics (Reidel, Dordrecht, The Netherlands, 1981).
[CrossRef]

Green, M. G.

M. G. Green, Spherical Astronomy (Cambridge U. Press, Cambridge, UK, 1985).

Hobbs, P. V.

J. M. Wallace, P. V. Hobbs, Atmospheric Science (Academic, London, 1977).

Hyvönen, V.

V. Antikainen, V. Hyvönen, “The accuracy of Vaisala RS 80 radiosonde,” in Proceedings of the Fifth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1983), pp. 134–140.

Iribarne, J. V.

J. V. Iribarne, W. L. Godson, Atmospheric Thermodynamics (Reidel, Dordrecht, The Netherlands, 1981).
[CrossRef]

Kattawar, G. W.

Lehn, W. H.

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, UK, 1995).

Lozowski, E. P.

R. D. Sampson, A. E. Peterson, E. P. Lozowski, “Photogrammetric calibration of a consumer grade flatbed scanner,” Geomatica (to be published).

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, UK, 1995).

Mahan, A. I.

Mahesh, A.

A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
[CrossRef]

McGlone, J. C.

J. C. McGlone, “Analytic data-reduction schemes in non-topographic photogrammetry,” in Non-Topographic Photogrammetry, 2nd ed., H. M. Karara, ed. (American Society for Photogrammetry and Remote Sensing, Washington, D.C., 1989).

Meeus, J.

J. Meeus, Astronomical Formulae for Calculators (Willmann-Bell, Richmond, Va., 1988).

Minnaert, M.

M. Minnaert, Light and Color in the Outdoors (Springer-Verlag, New York, 1993).
[CrossRef]

Oke, T. R.

T. R. Oke, Boundary Layer Climates (Methuen, London, 1987).

Parviainen, P.

Paukkenen, A.

A. Paukkenen, Vaisala Oyj, Helsinki, Finland, ari.paukkunen@vaisala.com (personal communications, 2000).

Peterson, A. E.

R. D. Sampson, A. E. Peterson, E. P. Lozowski, “Photogrammetric calibration of a consumer grade flatbed scanner,” Geomatica (to be published).

Press, W. H.

W. H. Press, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, UK, 1992).

Sampson, R.

R. Sampson, “Atmospheric refraction and sunrise and sunset,” Sky Telesc. 85, 96–97 (1993).

Sampson, R. D.

R. D. Sampson, “A comparison of photogrammetrically determined astronomical refraction of sunlight at high zenith angles with a ray-tracing computer model employing rawinsonde profiles,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 2000).

R. D. Sampson, “Atmospheric refraction and its effects on sunrise and sunset,” M.S. thesis (University of Alberta, Edmonton, Alberta, Canada, 1994).

R. D. Sampson, A. E. Peterson, E. P. Lozowski, “Photogrammetric calibration of a consumer grade flatbed scanner,” Geomatica (to be published).

Schmidlin, F. J.

F. J. Schmidlin, F. G. Finger, “Conclusions and recommendations resulting from the WMO international radiosonde intercomparison,” in Proceedings of the Sixth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1987), pp. 459–462.

Schwartz, B. E.

B. E. Schwartz, C. A. Doswell, “North American rawinsonde observations: problems, concerns, and a call to action,” Bull. Am. Meteorol. Soc. 72, 1885–1896 (1991).
[CrossRef]

Stull, R. B.

R. B. Stull, Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

Taylor, J. R.

J. R. Taylor, An Introduction to Error Analysis (University Science, Mill Valley, Calif., 1982).

Thom, A. A.

A. A. Thom, “An empirical investigation of atmospheric refraction,” Emp. Surv. Rev. 14, 248–262 (1958).
[CrossRef]

Von Walden, P.

A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
[CrossRef]

Wallace, J. M.

J. M. Wallace, P. V. Hobbs, Atmospheric Science (Academic, London, 1977).

Warren, S. G.

A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
[CrossRef]

Wilson, J. D.

T. K. Flesch, J. D. Wilson, “Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics,” Agri. For. Meteorol. 93, 243–258 (1998).
[CrossRef]

Wolf, P. R.

R. C. Brinker, P. R. Wolf, Elementary Surveying (Harper Row, New York, 1984).

P. R. Wolf, B. A. Dewitt, Elements of Photogrammetry (McGraw-Hill, Boston, 2000).

Young, A. T.

Agri. For. Meteorol. (1)

T. K. Flesch, J. D. Wilson, “Wind and remnant tree sway in forest cutblocks. II. Relating measured tree sway to wind statistics,” Agri. For. Meteorol. 93, 243–258 (1998).
[CrossRef]

Appl. Opt. (3)

Astron. J. (1)

G. M. Clemence, “Astronomical refraction at great zenith angles,” Astron. J. 56, 123–124 (1951).
[CrossRef]

Atmos. (1)

A. B. Fraser, “The green flash and clear air turbulence,” Atmos. 13, 1–10 (1975).

Bull. Am. Meteorol. Soc. (1)

B. E. Schwartz, C. A. Doswell, “North American rawinsonde observations: problems, concerns, and a call to action,” Bull. Am. Meteorol. Soc. 72, 1885–1896 (1991).
[CrossRef]

Emp. Surv. Rev. (1)

A. A. Thom, “An empirical investigation of atmospheric refraction,” Emp. Surv. Rev. 14, 248–262 (1958).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

A. Mahesh, P. Von Walden, S. G. Warren, “Radiosonde temperature measurements in strong inversions: correction for thermal lag based on an experiment at the South Pole,” J. Atmos. Ocean. Technol. 14, 45–53 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Sky Telesc. (1)

R. Sampson, “Atmospheric refraction and sunrise and sunset,” Sky Telesc. 85, 96–97 (1993).

Other (28)

V. Antikainen, V. Hyvönen, “The accuracy of Vaisala RS 80 radiosonde,” in Proceedings of the Fifth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1983), pp. 134–140.

J. R. Taylor, An Introduction to Error Analysis (University Science, Mill Valley, Calif., 1982).

M. G. Green, Spherical Astronomy (Cambridge U. Press, Cambridge, UK, 1985).

U.S. Standard Atmosphere (U.S. Government Printing Office, Washington, D.C., 1976).

A. Paukkenen, Vaisala Oyj, Helsinki, Finland, ari.paukkunen@vaisala.com (personal communications, 2000).

G. Bomford, Geodesy, 4th ed. (Clarendon, Oxford, UK, 1980).

R. C. Brinker, P. R. Wolf, Elementary Surveying (Harper Row, New York, 1984).

R. D. Sampson, “Atmospheric refraction and its effects on sunrise and sunset,” M.S. thesis (University of Alberta, Edmonton, Alberta, Canada, 1994).

“Scion image for windows,” Scion Corporation, Frederick, Md., 1999, http://www.scioncorp.com/index.htm .

J. C. McGlone, “Analytic data-reduction schemes in non-topographic photogrammetry,” in Non-Topographic Photogrammetry, 2nd ed., H. M. Karara, ed. (American Society for Photogrammetry and Remote Sensing, Washington, D.C., 1989).

W. H. Press, Numerical Recipes in FORTRAN (Cambridge U. Press, Cambridge, UK, 1992).

D. Carlsen, Winnipeg Office of Meteorological Services of Canada, Environment Canada, Winnipeg, Manitoba, Canada (personal communication, 2000).

“Mark II microsonde,” Sippican Inc., Marion, Mass., 1998, http://www.sippican.com/pdf/mark2.pdf .

F. J. Schmidlin, F. G. Finger, “Conclusions and recommendations resulting from the WMO international radiosonde intercomparison,” in Proceedings of the Sixth Symposium on Meteorological Observations and Instrumentation (American Meteorological Society, Boston, 1987), pp. 459–462.

M. Minnaert, Light and Color in the Outdoors (Springer-Verlag, New York, 1993).
[CrossRef]

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, UK, 1995).

S. P. Arya, Introduction to Micrometeorology (Academic, London, 1988).

R. B. Stull, Introduction to Boundary Layer Meteorology (Kluwer Academic, Dordrecht, The Netherlands, 1988).
[CrossRef]

P. R. Wolf, B. A. Dewitt, Elements of Photogrammetry (McGraw-Hill, Boston, 2000).

R. D. Sampson, A. E. Peterson, E. P. Lozowski, “Photogrammetric calibration of a consumer grade flatbed scanner,” Geomatica (to be published).

T. R. Oke, Boundary Layer Climates (Methuen, London, 1987).

Pulkovo Observatory, Refraction Tables of the Pulkovo Observatory, 5th ed. (Nauka, Leningrad, 1985).

“Vaisala product specifications” Vaisala Oyj, Helsinki, Finland, 1998, http://www.vaisala.fi .

J. Meeus, Astronomical Formulae for Calculators (Willmann-Bell, Richmond, Va., 1988).

R. D. Sampson, “A comparison of photogrammetrically determined astronomical refraction of sunlight at high zenith angles with a ray-tracing computer model employing rawinsonde profiles,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 2000).

D. Bruton, “Optical determination of atmospheric temperature profiles,” Ph.D. dissertation (Texas AM University, College Station, Texas, 1996).

J. M. Wallace, P. V. Hobbs, Atmospheric Science (Academic, London, 1977).

J. V. Iribarne, W. L. Godson, Atmospheric Thermodynamics (Reidel, Dordrecht, The Netherlands, 1981).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Star on the map of North America shows the general location of Edmonton. The larger map of the Edmonton area shows the location of the Henry Marshall Tory Building, the Stony Plain Upper Air Station, and two nearby surface weather stations. The two lines radiating from Stony Plain show the paths of the sunlight during the sunsets recorded in this experiment.

Fig. 2
Fig. 2

Plot shows the lower portion of the density gradient profile for the Stony Plain, Alberta, 8 December 1998, 23:15 UTC sounding. A Modified U.S. Standard Atmosphere (MUSSA) profile is also shown. The variation between the MUSSA and the U.S. Standard Atmosphere near the top of the graph is due to the difference in the height of the tropopause between the two model atmospheres.

Fig. 3
Fig. 3

Graph shows the planetary boundary layer’s density gradient profile for the 14 December 1998, 23:15 UTC sounding from the Stony Plain Upper Air Station (766 m above mean sea level). The U.S. Standard Atmosphere and MUSSA profiles are shown for comparison. Data for the observed profile was collected by use of a Vaisala RS80 rawinsonde system, which samples every 10 s. Dots represent the positive and negative uncertainties that are due to instrument error in the observed profile [±0.2 K, ±0.1 hPa, ±2% RH, and ±3 gpm (geopotential meters)]. These values were calculated by use of the error propagation method outlined in Taylor.36

Fig. 4
Fig. 4

Modeled refraction results are plotted with the observed position of the setting Sun for 8 December 1998 at 23:12:34.5 ± 0.2 s UTC. The model used the rawinsonde profiles and wavelengths of 530, 580, and 660 nm. The azimuthal wind offset was -1.3′.

Fig. 5
Fig. 5

Modeled refraction results are plotted with the observed position of the setting Sun for 14 December 1998 at 23:12:54.3 ± 0.2 s UTC. The model used the rawinsonde profiles and wavelengths of 530, 580, and 660 nm. The azimuthal wind offset was -0.72′.

Fig. 6
Fig. 6

Modeled refraction results are plotted with the observed position of the setting Sun for 22 December 1998 at 23:12:28.7 ± 0.1 s UTC. The model used the rawinsonde profiles and wavelengths of 530, 580, and 660 nm. The azimuthal wind offset was -1.2′.

Fig. 7
Fig. 7

Observed refraction of the top of the Sun minus modeled refraction for yellow light from both Stony Plain and the H. M. Tory Building at the University of Alberta (dashed curves). The arc at the top of the graph is used for scale and represents the disk of the Sun (D ∼ 32′ along the vertical scale).

Fig. 8
Fig. 8

Same situation as in Fig. 4 (8 December sounding) except the model used a MUSSA profile.

Fig. 9
Fig. 9

Same situation as in Fig. 5 (14 December sounding) except the model used a MUSSA profile.

Fig. 10
Fig. 10

Same situation as in Fig. 6 (22 December sounding) except the model used a MUSSA profile.

Tables (1)

Tables Icon

Table 1 Comparison of the rms Difference between the Observed and the Modeled Refraction (Yellow Light)a

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

κ=cos βnΔnΔr,
Rt=kdre,
k=252pT20.0342+dTdz,
Y=Xxf,
Z=Xyf,
|Δz|=-3.83 lnp + 26.85,

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