Abstract

The direct and diffuse components of downwelling irradiance have in general different path lengths in water, and hence they decrease differently with sensor depth. Furthermore, the ever-changing geometry of a wind-roughened and wave-modulated water surface induces uncorrelated intensity changes to these components. To cope with both effects, an analytic model of the downwelling irradiance in water was developed that calculates the direct and diffuse components separately. By assigning weights fdd and fds to the intensities of the two components, measurements performed at arbitrary surface conditions can be analyzed by treating fdd and fds as fit parameters. The model was validated against HydroLight and implemented into the public-domain software WASI. It was applied to data from three German lakes to determine the statistics of fdd and fds, to derive the sensor depth of each measurement and to estimate the concentrations of water constituents.

© 2012 Optical Society of America

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References

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2011 (2)

2008 (2)

H. Hofmann, A. Lorke, and F. Peeters, “Wave-induced variability of the underwater light climate in the littoral zone,” Verh. Internat. Verein. Limnol. 30, 627–632 (2008).

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

2007 (1)

R. Doerffer and H. Schiller, “The MERIS Case 2 water algorithm,” Int. J. Remote Sens. 28, 517–535 (2007).
[CrossRef]

2004 (1)

P. Gege, “The water color simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra,” Comput. Geosci. 30, 523–532 (2004).
[CrossRef]

2001 (1)

2000 (2)

1994 (1)

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994).
[CrossRef]

1993 (2)

1992 (1)

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

1990 (1)

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

1989 (3)

F. Kasten and A. T. Young, “Revised optical air mass tables and approximation formula,” Appl. Opt. 28, 4735–4738 (1989).
[CrossRef]

H. R. Gordon, “Can the Lambert–Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr. 34, 1389–1409 (1989).
[CrossRef]

K. L. Carder, G. R. Harvey, and P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

1986 (1)

J. Dera and D. Stramski, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).

1984 (1)

M. S. Caceci and W. P. Cacheris, “Fitting curves to data,” Byte 9, 340–362 (1984).

1981 (1)

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

1980 (1)

T. I. Quickenden and J. A. Irvin, “The ultraviolet absorption spectrum of liquid water,” J. Chem. Phys. 72, 4416–4428 (1980).
[CrossRef]

1974 (1)

K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. A 64, 1107–1110 (1974).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

1954 (2)

C. Cox and W. Munk, “The measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Abreu, L. W.

F. X. Kneizys, L. W. Abreu, and G. P. Anderson, “The MODTRAN 2/3 Report and LOWTRAN 7 MODEL,” Technical report, Phillips Laboratory, Geophysics Directorate, Hanscom, Massachusetts (1996).

Albert, A.

P. Gege and A. Albert, “A tool for inverse modeling of spectral measurements in deep and shallow waters,” in Remote Sensing of Aquatic Coastal Ecosystem Processes: Science and Management Applications, L. L. Richardson and E. F. LeDrew, eds. (Springer, 2006), pp. 81–109.

Anderson, G. P.

F. X. Kneizys, L. W. Abreu, and G. P. Anderson, “The MODTRAN 2/3 Report and LOWTRAN 7 MODEL,” Technical report, Phillips Laboratory, Geophysics Directorate, Hanscom, Massachusetts (1996).

Barnard, A.

Barrow, T.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Benner, D. C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Boss, E.

Bricaud, A.

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

Brown, L. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Buiteveld, H.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994).
[CrossRef]

Bukata, R.

R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC, 1995).

Caceci, M. S.

M. S. Caceci and W. P. Cacheris, “Fitting curves to data,” Byte 9, 340–362 (1984).

Cacheris, W. P.

M. S. Caceci and W. P. Cacheris, “Fitting curves to data,” Byte 9, 340–362 (1984).

Camy-Peyret, C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Carder, K. L.

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

K. L. Carder, G. R. Harvey, and P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Cox, C.

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

C. Cox and W. Munk, “The measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

Dall’Olmo, G.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Dera, J.

J. Dera and D. Stramski, “Focusing of sunlight by sea surface waves: new results from the Black Sea,” Oceanologia 34, 13–25 (1993).

J. Dera and D. Stramski, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).

Doerffer, R.

R. Doerffer and H. Schiller, “The MERIS Case 2 water algorithm,” Int. J. Remote Sens. 28, 517–535 (2007).
[CrossRef]

Donze, M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994).
[CrossRef]

Fisher, T. R.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Flaud, J.-M.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Gamache, R. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Gege, P.

P. Gege and N. Pinnel, “Sources of variance of downwelling irradiance in water,” Appl. Opt. 50, 2192–2203 (2011).
[CrossRef]

P. Gege, “The water color simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra,” Comput. Geosci. 30, 523–532 (2004).
[CrossRef]

P. Gege, “Estimation of phytoplankton concentration from downwelling irradiance measurements in water,” Israel J. Plant Sci. (to be published).

P. Gege, “Characterization of the phytoplankton in Lake Constance for classification by remote sensing,” in Lake Constance—Characterisation of an Ecosystem in Transition, E. Bäuerle and U. Gaedke, eds. (Archiv für Hydrobiologie53, 1998), pp. 179–193.

P. Gege and A. Albert, “A tool for inverse modeling of spectral measurements in deep and shallow waters,” in Remote Sensing of Aquatic Coastal Ecosystem Processes: Science and Management Applications, L. L. Richardson and E. F. LeDrew, eds. (Springer, 2006), pp. 81–109.

Gentili, B.

Gitelson, A. A.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Goldman, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Gordon, H. R.

Gregg, W. W.

W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
[CrossRef]

Gurlin, D.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Hakvoort, J. H. M.

H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994).
[CrossRef]

Harvey, G. R.

K. L. Carder, G. R. Harvey, and P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Heege, T.

T. Heege, “Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen am Bodensee,” Ph.D. thesis (DLR-Forschungsbericht, 2000).

Hofmann, H.

H. Hofmann, A. Lorke, and F. Peeters, “Wave-induced variability of the underwater light climate in the littoral zone,” Verh. Internat. Verein. Limnol. 30, 627–632 (2008).

Holz, J.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Hooker, S. B.

S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Oceanic Technol. 17, 811–830 (2000).

Irvin, J. A.

T. I. Quickenden and J. A. Irvin, “The ultraviolet absorption spectrum of liquid water,” J. Chem. Phys. 72, 4416–4428 (1980).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, 1976).

Jerome, J. H.

R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC, 1995).

Jin, Z.

Kasten, F.

Kattawar, G. W.

Kneizys, F. X.

F. X. Kneizys, L. W. Abreu, and G. P. Anderson, “The MODTRAN 2/3 Report and LOWTRAN 7 MODEL,” Technical report, Phillips Laboratory, Geophysics Directorate, Hanscom, Massachusetts (1996).

Kondratyev, K. Y.

R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC, 1995).

Lorke, A.

H. Hofmann, A. Lorke, and F. Peeters, “Wave-induced variability of the underwater light climate in the littoral zone,” Verh. Internat. Verein. Limnol. 30, 627–632 (2008).

Malathy Devi, V.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Maritorena, S.

S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Oceanic Technol. 17, 811–830 (2000).

Massie, S. T.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Menzies, D. W.

Mobley, C. D.

Morel, A.

C. D. Mobley, B. Gentili, H. R. Gordon, Z. Jin, G. W. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. Stavn, “Comparison of numerical models for the computation of underwater light fields,” Appl. Opt. 32, 7484–7504 (1993).
[CrossRef]

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
[CrossRef]

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N. G. Jerlov and E. Steemann Nielsen, eds. (Academic, 1997), pp. 1–24.

Moses, W.

A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
[CrossRef]

Mueller, J. L.

J. L. Mueller, “In-water radiometric profile measurements and data analysis protocols,” in Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 4, Vol. III, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA, 2003), pp. 7–20.

Munk, W.

C. Cox and W. Munk, “The measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
[CrossRef]

C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Neumann, M. J.

Ortner, P. B.

K. L. Carder, G. R. Harvey, and P. B. Ortner, “Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll,” Limnol. Oceanogr. 34, 68–81 (1989).
[CrossRef]

Palmer, K. F.

K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. A 64, 1107–1110 (1974).
[CrossRef]

Peeters, F.

H. Hofmann, A. Lorke, and F. Peeters, “Wave-induced variability of the underwater light climate in the littoral zone,” Verh. Internat. Verein. Limnol. 30, 627–632 (2008).

Perrin, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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P. Gege and N. Pinnel, “Sources of variance of downwelling irradiance in water,” Appl. Opt. 50, 2192–2203 (2011).
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Prieur, L.

A. Bricaud, A. Morel, and L. Prieur, “Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domains,” Limnol. Oceanogr. 26, 43–53 (1981).
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T. I. Quickenden and J. A. Irvin, “The ultraviolet absorption spectrum of liquid water,” J. Chem. Phys. 72, 4416–4428 (1980).
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L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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A. A. Gitelson, G. Dall’Olmo, W. Moses, D. C. Rundquist, T. Barrow, T. R. Fisher, D. Gurlin, and J. Holz, “A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: validation,” Remote Sens. Environ. 112, 3582–3593 (2008).
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L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
[CrossRef]

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Toth, R. A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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P. Gege, “The water color simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra,” Comput. Geosci. 30, 523–532 (2004).
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R. Doerffer and H. Schiller, “The MERIS Case 2 water algorithm,” Int. J. Remote Sens. 28, 517–535 (2007).
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P. Gege, “Estimation of phytoplankton concentration from downwelling irradiance measurements in water,” Israel J. Plant Sci. (to be published).

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S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Oceanic Technol. 17, 811–830 (2000).

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K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. A 64, 1107–1110 (1974).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer 48, 469–507 (1992).
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H. Hofmann, A. Lorke, and F. Peeters, “Wave-induced variability of the underwater light climate in the littoral zone,” Verh. Internat. Verein. Limnol. 30, 627–632 (2008).

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Figures (13)

Fig. 1.
Fig. 1.

Atmospheric transmission after absorption by ozone, oxygen, and water vapor.

Fig. 2.
Fig. 2.

Effective absorption coefficients of the atmospheric components ozone, oxygen, and water vapor.

Fig. 3.
Fig. 3.

Comparison of analytically estimated sensor depths with results from inverse modeling.

Fig. 4.
Fig. 4.

Extraterrestrial solar irradiance.

Fig. 5.
Fig. 5.

Comparison of above water irradiance spectra for θ sun = 30 ° .

Fig. 6.
Fig. 6.

Dependency of the reflectance factor for diffuse irradiance on the Sun zenith angle.

Fig. 7.
Fig. 7.

Dependency of the relative path length of diffuse radiation on depth and on the Sun zenith angle.

Fig. 8.
Fig. 8.

Comparison of spectral shape for WASI4 and HE5 simulations of irradiance.

Fig. 9.
Fig. 9.

Comparison of intensity for WASI4 and HE5 simulations of irradiance.

Fig. 10.
Fig. 10.

Example for inverse modeling of an irradiance measurement. Fit parameters: X = 0.85 g m 3 , Y = 0.21 m 1 , f d d = 1.02 , f d s = 1.02 , z = 1.06 m . (a) Measured spectrum and model curve. (b) Direct and diffuse component obtained from inverse modeling.

Fig. 11.
Fig. 11.

Frequency distributions of the parameters f d d and f d s .

Fig. 12.
Fig. 12.

Variability of the ratio of direct to diffuse irradiance.

Fig. 13.
Fig. 13.

Sensor depth variability during a measurement.

Tables (2)

Tables Icon

Table 1. Parameters of the Irradiance Model That Can Be Used in WASI as Fit Parameters

Tables Icon

Table 2. Mean and Standard Deviation of Suspended Matter Concentration ( X , σ X ) and Gelbstoff Concentration ( Y , σ Y ) Derived by Inverse Modeling of Measurements at Depths > 1.5 m

Equations (27)

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

E d ( λ , z ) = f d d E d d ( λ , z ) + f d s E d s ( λ , z ) .
E d d ( λ , z ) = E d s ( λ , 0 ) exp { K d s ( λ ) z l d s } .
E d d ( λ , z ) = E d d ( λ , 0 ) exp { K d d ( λ ) z l d d cos θ sun } ·
ρ d d = 1 2 | sin 2 ( θ sun θ sun ) sin 2 ( θ sun + θ sun ) + tan 2 ( θ sun θ sun ) tan 2 ( θ sun + θ sun ) | ,
ρ d s = 0.06087 + 0.03751 ( 1 cos θ sun ) + 0.1143 ( 1 cos θ sun ) 2 .
E d d ( λ , 0 ) = F 0 ( λ ) cos θ sun T r ( λ ) T a a ( λ ) T a s ( λ ) T oz ( λ ) T o ( λ ) T wv ( λ ) ( 1 ρ d d ) .
E d s ( λ , 0 ) = [ E d r ( λ ) + E d a ( λ ) ] ( 1 ρ d s ) .
E d r ( λ ) = 1 2 F 0 ( λ ) cos θ sun ( 1 T r ( λ ) 0.95 ) T a a ( λ ) T oz ( λ ) T o ( λ ) T wv ( λ ) ,
E d a ( λ ) = F 0 ( λ ) cos θ sun T r ( λ ) 1.5 T a a ( λ ) T oz ( λ ) T o ( λ ) T wv ( λ ) ( 1 T a s ( λ ) ) F a .
T a a ( λ ) = exp [ ( 1 ω a ) τ a ( λ ) M ] ,
T a s ( λ ) = exp [ ω a τ a ( λ ) M ] ,
T r ( λ ) = exp [ M / ( 115.6406 λ 4 1.335 λ 2 ) ] ,
T oz ( λ ) = exp [ a oz ( λ ) H oz M oz ] ,
T o ( λ ) = exp 1.41 a o ( λ ) · M [ 1 + 118.3 a o ( λ ) · M ] 0.45 ,
T wv ( λ ) = exp 0.2385 a wv ( λ ) · W V · M [ 1 + 20.07 a wv ( λ ) · W V · M ] 0.45 .
r d ( λ , 0 ) = f d d f d s E d d ( λ , 0 ) E d s ( λ , 0 ) = f d d f d s 2 T r ( λ ) T as ( λ ) ( 1 ρ d d ) [ 1 T r ( λ ) 0.95 + 2 T r ( λ ) 1.5 ( 1 T as ( λ ) ) F a ] ( 1 ρ d s ) .
r d ( λ , z ) = f d d f d s E d d ( λ , z ) E d s ( λ , z ) = f d d f d s E d d ( λ , 0 ) exp { K d d ( λ ) z l d d / cos θ sun } E d s ( λ , 0 ) exp { K d s ( λ ) z l d s }
r d ( λ , z ) = r d ( λ , 0 ) exp { ( K d s ( λ ) l d s K d d ( λ ) l d d cos θ sun ) z } .
K d s ( λ ) = K d d ( λ ) = a ( λ ) + b b ( λ ) ,
a ( λ ) = a W ( λ ) + a ph ( λ ) + a Y ( λ ) + a d ( λ ) ,
b b ( λ ) = b b , W ( λ ) + b b , X ( λ ) ,
a ph ( λ ) = C i a i * ( λ ) .
b b , X ( λ ) = X · b b , X * · b X ( λ ) + C Mie · b b , Mie * · ( λ / λ S ) n .
l d s = 1.1156 + 0.5504 ( 1 cos θ sun ) ,
l d d = 1.
z 0 = g cos θ sun ln r ln r ( 0 ) K d d ( λ 2 ) K d d ( λ 1 ) .
l d s = 1 [ a ( λ ) + b b ( λ ) ] z ln E d s ( λ , z , θ sun ) E d s ( λ , 0 , θ sun ) ·

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