Abstract

Variation of the atmospheric refraction index due to turbulent fluctuations is one of the key factors that affect the performance of electro-optical and infrared systems and sensors. Therefore, any prior knowledge about the degree of variation in the refractive index is critical in the success of field studies such as search and rescue missions, military applications, and remote sensing studies where these systems are used frequently. There are many studies in the literature in which the optical turbulence effects are modeled by estimation of the refractive index structure parameter, Cn2, from meteorological data for all levels of the atmosphere. This paper presents a modified approach for bulk-method-based Cn2 estimation. According to this approach, conventional wind speed, humidity, and temperature values above the surface by at least two levels are used as input data for Monin–Obukhov similarity theory in the estimation of similarity scaling constants with a finite difference approximation and a bulk-method-based Cn2 estimation. Compared with the bulk method, this approach provides the potential for using more than two levels of standard meteorological data, application of the scintillation effects of estimated Cn2 on the images, and a much simpler solution than traditional ones due to elimination of the roughness parameters, which are difficult to obtain and which increase the complexity, the execution time, and the number of additional input parameters of the algorithm. As a result of these studies, Atmospheric Turbulence Model Software is developed and the results are validated in comparison to the Cn2 model presented by Tunick.

© 2013 Optical Society of America

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  1. V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).
  2. A. Tunick, “Optical turbulence parameters characterized via optical measurements over a 2.33 km free-space laser path,” Opt. Express 16, 14645–14654 (2008).
    [CrossRef]
  3. A. Tunick, “CN2 model to calculate the micrometeorological influences on the refractive index structure parameter,” Environ. Modell. Software 18, 165–171 (2003).
    [CrossRef]
  4. H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteorol. 33, 964–976 (1994).
    [CrossRef]
  5. E. L. Andreas, “Estimating Cn2 over snow and sea ice from meteorological data,” J. Opt. Soc. Am. A 5, 481–495 (1988).
    [CrossRef]
  6. P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).
  7. G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
    [CrossRef]
  8. K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, “Verification of the bulk model for calculating over-water optical turbulence,” Appl. Opt. 20, 2919–2929 (1981).
    [CrossRef]
  9. G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
    [CrossRef]
  10. P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
    [CrossRef]
  11. W. P. Cole and M. A. Marciniak, “Path-averaged Cn2 estimation using a laser-and-corner-cube system,” Appl. Opt. 48, 4256–4262 (2009).
    [CrossRef]
  12. S. Bendersky, N. S. Kopeika, and N. Blaunstein, “Atmospheric optical turbulence over land in Middle East coastal environments: prediction modeling and measurements,” Appl. Opt. 43, 4070–4079 (2004).
    [CrossRef]
  13. A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007).
    [CrossRef]
  14. M. P. Chang, C. O. Font, G. C. Gilbreath, and E. Oh, “Humidity’s influence on visible region refractive index structure parameter C(n)(2),” Appl. Opt. 46, 2453–2459 (2007).
    [CrossRef]
  15. Y. Jiang, J. Ma, L. Tan, S. Yu, and W. Du, “Measurement of optical intensity fluctuation over an 11.8 km turbulent path,” Opt. Express 16, 6963–6973 (2008).
    [CrossRef]
  16. F. S. Vetelino, K. Grayshan, and C. Y. Young, “Inferring path average Cn2 values in the marine environment,” J. Opt. Soc. Am. A 24, 3198–3206 (2007).
    [CrossRef]
  17. A. S. Monin and A. M. Obukhov, “Basic regularity in turbulent mixing in the surface layer of the atmosphere,” Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR 24, 163–187 (1954).
  18. C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
    [CrossRef]
  19. C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
    [CrossRef]
  20. A. J. Dyer, “A review of flux–profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
    [CrossRef]
  21. W. K. Webb, “Profile relationships: the log–linear range and extension to strong stability,” Q. J. R. Meteorol. Soc. 96, 67–90 (1970).
    [CrossRef]
  22. C. J. Owens, “Optical refractive index of air; dependence on pressure temperature and composition,” Appl. Opt. 6, 51–59(1967).
    [CrossRef]
  23. R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
    [CrossRef]
  24. J. C. Wyngaard, Y. Izumi, and S. A. Collins, “Behavior of the refractive-index-structure parameter near the ground,” J. Opt. Soc. Am. 61, 1646–1650 (1971).
    [CrossRef]
  25. C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
    [CrossRef]
  26. W. Kohsiek, “Measuring CT2, Cq2 and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
    [CrossRef]
  27. J. B. Edson and C. W. Fairall, “Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets,” J. Atmos. Sci. 55, 2311–2328 (1998).
    [CrossRef]
  28. E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).
  29. H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
    [CrossRef]
  30. A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
    [CrossRef]
  31. A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
    [CrossRef]
  32. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  33. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1431(1965).
    [CrossRef]
  34. R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” J. Opt. Soc. Am. 54, 52–60 (1964).
    [CrossRef]
  35. J. Goodman, Statistical Optics (Wiley, 1985).
  36. I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
    [CrossRef]
  37. K. Buskila, S. Towito, E. Shmuel, R. Levi, N. Kopeika, K. Krapels, R. G. Driggers, R. H. Vollmerhausen, and C. E. Halford, “Atmospheric modulation transfer function in the infrared,” Appl. Opt. 43, 471–482 (2004).
    [CrossRef]

2009 (1)

2008 (2)

2007 (4)

P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
[CrossRef]

F. S. Vetelino, K. Grayshan, and C. Y. Young, “Inferring path average Cn2 values in the marine environment,” J. Opt. Soc. Am. A 24, 3198–3206 (2007).
[CrossRef]

A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007).
[CrossRef]

M. P. Chang, C. O. Font, G. C. Gilbreath, and E. Oh, “Humidity’s influence on visible region refractive index structure parameter C(n)(2),” Appl. Opt. 46, 2453–2459 (2007).
[CrossRef]

2005 (1)

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

2004 (2)

2003 (1)

A. Tunick, “CN2 model to calculate the micrometeorological influences on the refractive index structure parameter,” Environ. Modell. Software 18, 165–171 (2003).
[CrossRef]

2000 (1)

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

1998 (2)

J. B. Edson and C. W. Fairall, “Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets,” J. Atmos. Sci. 55, 2311–2328 (1998).
[CrossRef]

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

1996 (2)

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

1995 (2)

H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
[CrossRef]

I. Dror and N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
[CrossRef]

1994 (2)

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteorol. 33, 964–976 (1994).
[CrossRef]

1988 (1)

1986 (1)

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

1982 (1)

W. Kohsiek, “Measuring CT2, Cq2 and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

1981 (1)

1980 (1)

C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

1977 (1)

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

1974 (1)

A. J. Dyer, “A review of flux–profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
[CrossRef]

1971 (1)

1970 (2)

W. K. Webb, “Profile relationships: the log–linear range and extension to strong stability,” Q. J. R. Meteorol. Soc. 96, 67–90 (1970).
[CrossRef]

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
[CrossRef]

1967 (1)

1966 (1)

1965 (1)

1964 (1)

1954 (1)

A. S. Monin and A. M. Obukhov, “Basic regularity in turbulent mixing in the surface layer of the atmosphere,” Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR 24, 163–187 (1954).

Andreas, E. L.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

E. L. Andreas, “Estimating Cn2 over snow and sea ice from meteorological data,” J. Opt. Soc. Am. A 5, 481–495 (1988).
[CrossRef]

Bendall, C. S.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

Bendersky, S.

Blaunstein, N.

Bradley, E. F.

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

Buskila, K.

Chang, M. P.

Cole, W. P.

Collins, S. A.

Davidson, K. L.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, “Verification of the bulk model for calculating over-water optical turbulence,” Appl. Opt. 20, 2919–2929 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

de Leeuw, G.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

Driggers, R. G.

Dror, I.

Du, W.

Dyer, A. J.

A. J. Dyer, “A review of flux–profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
[CrossRef]

Edson, J. B.

J. B. Edson and C. W. Fairall, “Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets,” J. Atmos. Sci. 55, 2311–2328 (1998).
[CrossRef]

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

Evett, S. R.

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Fairall, C. W.

J. B. Edson and C. W. Fairall, “Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets,” J. Atmos. Sci. 55, 2311–2328 (1998).
[CrossRef]

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, “Verification of the bulk model for calculating over-water optical turbulence,” Appl. Opt. 20, 2919–2929 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

Font, C. O.

Frederickson, P. A.

P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
[CrossRef]

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

Fried, D. L.

Fritz, P. J.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

Gilbreath, G. C.

Goodman, J.

J. Goodman, Statistical Optics (Wiley, 1985).

Goroch, A. K.

Gosz, J. R.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

Grayshan, K.

Halford, C. E.

Hammel, S.

P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
[CrossRef]

Hammel, S. M.

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

Hansen, F. V.

H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
[CrossRef]

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Hill, R. J.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

Howell, T. A.

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Hufnagel, R. E.

Izumi, Y.

Jiang, Y.

Kohsiek, W.

W. Kohsiek, “Measuring CT2, Cq2 and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

Kopeika, N.

Kopeika, N. S.

Krapels, K.

Kunz, G. J.

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

Lawrence, R. S.

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

Levi, R.

Ma, J.

Marciniak, M. A.

Moerman, M. M.

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

Monin, A. S.

A. S. Monin and A. M. Obukhov, “Basic regularity in turbulent mixing in the surface layer of the atmosphere,” Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR 24, 163–187 (1954).

Moore, D. I.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

Obukhov, A. M.

A. S. Monin and A. M. Obukhov, “Basic regularity in turbulent mixing in the surface layer of the atmosphere,” Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR 24, 163–187 (1954).

Oh, E.

Otto, W. D.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

Owens, C. J.

Paulson, C. A.

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
[CrossRef]

Rachele, H.

H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
[CrossRef]

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteorol. 33, 964–976 (1994).
[CrossRef]

Rogers, D. P.

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

Sarma, A. D.

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

Schacher, G. E.

K. L. Davidson, G. E. Schacher, C. W. Fairall, and A. K. Goroch, “Verification of the bulk model for calculating over-water optical turbulence,” Appl. Opt. 20, 2919–2929 (1981).
[CrossRef]

C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

Schneider, A. D.

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Shmuel, E.

Stanley, N. R.

Steiner, J. L.

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Tan, L.

Tatarski, V. I.

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

Towito, S.

Tsintikidis, D.

P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
[CrossRef]

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

Tunick, A.

A. Tunick, “Optical turbulence parameters characterized via optical measurements over a 2.33 km free-space laser path,” Opt. Express 16, 14645–14654 (2008).
[CrossRef]

A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007).
[CrossRef]

A. Tunick, “CN2 model to calculate the micrometeorological influences on the refractive index structure parameter,” Environ. Modell. Software 18, 165–171 (2003).
[CrossRef]

H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
[CrossRef]

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteorol. 33, 964–976 (1994).
[CrossRef]

van Eijk, A. M. J.

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

Vetelino, F. S.

Vollmerhausen, R. H.

Webb, W. K.

W. K. Webb, “Profile relationships: the log–linear range and extension to strong stability,” Q. J. R. Meteorol. Soc. 96, 67–90 (1970).
[CrossRef]

Wyngaard, J. C.

Yaglom, A. M.

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

Young, C. Y.

Young, G. S.

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

Yu, S.

Zeisse, C. R.

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

Appl. Opt. (6)

Boundary-Layer Meteorol. (5)

E. L. Andreas, R. J. Hill, J. R. Gosz, D. I. Moore, W. D. Otto, and A. D. Sarma, “Statistics of surface-layer turbulence over terrain with meter-scale heterogeneity,” Boundary-Layer Meteorol. 86, 379–408 (1998).

A. J. Dyer, “A review of flux–profile relationships,” Boundary-Layer Meteorol. 7, 363–372 (1974).
[CrossRef]

C. W. Fairall, G. E. Schacher, and K. L. Davidson, “Measurements of the humidity structure function parameters, Cq2 and CTq, over the ocean,” Boundary-Layer Meteorol. 19, 81–92 (1980).
[CrossRef]

W. Kohsiek, “Measuring CT2, Cq2 and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture,” Boundary-Layer Meteorol. 24, 89–107 (1982).
[CrossRef]

A. M. Yaglom, “Comments on wind and temperature flux-profile relationships,” Boundary-Layer Meteorol. 11, 89–102 (1977).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

A. Tunick, H. Rachele, F. V. Hansen, T. A. Howell, J. L. Steiner, A. D. Schneider, and S. R. Evett, “REBAL ‘92-A cooperative radiation and energy balance field study for imagery and EM propagation,” Bull. Am. Meteorol. Soc. 75, 421–430 (1994).
[CrossRef]

Environ. Modell. Software (1)

A. Tunick, “CN2 model to calculate the micrometeorological influences on the refractive index structure parameter,” Environ. Modell. Software 18, 165–171 (2003).
[CrossRef]

Infrared Phys. (1)

R. J. Hill and R. S. Lawrence, “Refractive index of water vapor in infrared windows,” Infrared Phys. 26, 371–376 (1986).
[CrossRef]

J. Appl. Meteorol. (4)

H. Rachele and A. Tunick, “Energy balance model for imagery and electromagnetic propagation,” J. Appl. Meteorol. 33, 964–976 (1994).
[CrossRef]

P. A. Frederickson, K. L. Davidson, C. R. Zeisse, and C. S. Bendall, “Estimating the refractive index structure parameter (Cn2) over the ocean using bulk methods,” J. Appl. Meteorol. 39, 1770–1783 (2000).

H. Rachele, A. Tunick, and F. V. Hansen, “MARIAH-A similarity based method for determining wind, temperature and humidity profile structure in the atmospheric surface layer,” J. Appl. Meteorol. 34, 1000–1005 (1995).
[CrossRef]

C. A. Paulson, “The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer,” J. Appl. Meteorol. 9, 857–861 (1970).
[CrossRef]

J. Atmos. Sci. (1)

J. B. Edson and C. W. Fairall, “Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets,” J. Atmos. Sci. 55, 2311–2328 (1998).
[CrossRef]

J. Geophys. Res. (1)

C. W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, “Bulk parameterization of sea-air fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment,” J. Geophys. Res. 101, 3747–3764 (1996).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Meteorol. Atmos. Phys. (1)

A. Tunick, “Modeling microphysical influences on optical turbulence in complex areas,” Meteorol. Atmos. Phys. 96, 293–304 (2007).
[CrossRef]

Opt. Express (2)

Proc. SPIE (3)

G. J. Kunz, M. M. Moerman, P. J. Fritz, and G. de Leeuw, “Validation of a bulk turbulence model with thermal images of a point source,” Proc. SPIE 2828, 108–116 (1996).
[CrossRef]

G. J. Kunz, A. M. J. van Eijk, D. Tsintikidis, and S. M. Hammel, “Effects of atmospheric refraction and turbulence on long-range IR imaging in the marine surface layer: comparisons between experiment and simulation,” Proc. SPIE 5891, 58910A (2005).
[CrossRef]

P. A. Frederickson, S. Hammel, and D. Tsintikidis, “Improving bulk Cn2 models for over-ocean applications through new determinations of the dimensionless temperature structure parameter,” Proc. SPIE 6708, 670807 (2007).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

W. K. Webb, “Profile relationships: the log–linear range and extension to strong stability,” Q. J. R. Meteorol. Soc. 96, 67–90 (1970).
[CrossRef]

Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR (1)

A. S. Monin and A. M. Obukhov, “Basic regularity in turbulent mixing in the surface layer of the atmosphere,” Trans. Geophys. Inst. (Trudy) Acad. Sci. USSR 24, 163–187 (1954).

Other (2)

V. I. Tatarski, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

J. Goodman, Statistical Optics (Wiley, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

Cn2 values obtained using input data given in Table 1 for the models ATMSOFT (star and diamond) and Tunick (downward triangle and circle) with MARIAH and OKEYPS methodologies.

Fig. 2.
Fig. 2.

Example of ATMSOFT Cn2 model formatted output.

Fig. 3.
Fig. 3.

Example of scintillation effects of Cn2 for LWIR wavelength band images measured by FLIR A40M infrared camera; (a) original and (b) with modeled atmospheric effects where Cn2>1014m2/3.

Tables (1)

Tables Icon

Table 1. ATMSOFT Cn2 Model Input Parameters and Range Boundaries

Equations (20)

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U*2=UW,T*=TW/U*,Q*=QW/U*,
L=θvirU*2/[kg(T*+0.61TQ*)],
U(z)=U0+(U*/k)[ln(z/zu)ψm(ζ)],T(z)=T0+(T*/k)[ln(z/zT)ψh(ζ)],Q(z)=Q0+(Q*/k)[ln(z/zQ)ψw(ζ)],
ψm(ζ)=2ln[(1+x)/2]+ln[(1+x2)/2]2arctan(x)+π/2,ψh(ζ)=2ln[(1+x2)/2],ψw(ζ)=ψh(ζ),
ψm(ζ)=ψw(ζ)=ψh(ζ)=5ζ.
φ(z)/zφ(z+Δz)φ(zΔz)/2Δz;φ=U,T,Q.
U*=k(U(z2)U(z1))[ln(z2/z1)ψm(ζ2)+ψm(ζ1)]1,T*=k(T(z2)T(z1))[ln(z2/z1)ψh(ζ2)+ψh(ζ1)]1,Q*=k(Q(z2)Q(z1))[ln(z2/z1)ψw(ζ2)+ψw(ζ1)]1,
Cn2=A2CT2+2ABCTQ+B2CQ2.
nv=1+106[m1(λ)(p/t)+4.615[m2(λ)m1(λ)]q],
m1(λ)=23.7134+6839.397130λ2+45.47338.9λ2,m2(λ)=64.8731+0.58058λ20.0071150λ4+0.0008851λ6,
n=A(λ,P,T,Q)t+B(λ,P,T,Q)q,
ni=1+106[nvd+niw],
nvd=[m1(λ)(p/t)+4.615m1(λ)q].
niw=q[957928θ0.4(χ1)1.03θ0.1719.8χ2+8.2χ41.7χ8+3.747×10612499χ2],
Ai=Avd+Aiw,Bi=Bvd+Biw,
Avd=106m1(λ)p/t2,Bvd=4.6150×106m1(λ),Aiw=106q[1.359θ0.6(χ1)H1[0.6135θ0.83+0.5949θ0.43(χ1)]H2],Biw=106[957928θ0.4(χ1)]H1+3.747/(12449χ2),
CT2=T*2gT(ζ)z2/3,CQ2=Q*2gQ(ζ)z2/3,CTQ=T*Q*gTQ(ζ)z2/3,
gT(ζ)=gQ(ζ)=gTQ(ζ)={4.9(16.1ζ)2/3ζ04.9(1+2.2ζ2/3)ζ0.
MTF=e3.44(λfRr0)53[1α(λfRD)13],
r0=0.185[λ2secβh0HCn2(h)dh]35,

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