Analytic model for the direct and diffuse components of downwelling spectral irradiance in water

doi:10.1364/AO.51.001407

Analytic model for the direct and diffuse components of downwelling spectral irradiance in water

Peter Gege »View Author Affiliations

Applied Optics, Vol. 51, Issue 9, pp. 1407-1419 (2012)
http://dx.doi.org/10.1364/AO.51.001407

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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 $f_{d d}$ and $f_{d s}$ to the intensities of the two components, measurements performed at arbitrary surface conditions can be analyzed by treating $f_{d d}$ and $f_{d s}$ 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 $f_{d d}$ and $f_{d s}$ , to derive the sensor depth of each measurement and to estimate the concentrations of water constituents.

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(300.0300) Spectroscopy : Spectroscopy
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(010.5620) Atmospheric and oceanic optics : Radiative transfer

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: August 29, 2011
Revised Manuscript: December 6, 2011
Manuscript Accepted: December 27, 2011
Published: March 20, 2012

Virtual Issues
Vol. 7, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Peter Gege, "Analytic model for the direct and diffuse components of downwelling spectral irradiance in water," Appl. Opt. 51, 1407-1419 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-9-1407

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References

R. E. Walker, Marine Light Field Statistics (Wiley, 1994).
J. R. V. Zanefeld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001). [CrossRef]
J. Dera and D. Stramski, “Focusing of sunlight by sea surface waves: new results from the Black Sea,” Oceanologia 34, 13–25 (1993).
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).
P. Gege and N. Pinnel, “Sources of variance of downwelling irradiance in water,” Appl. Opt. 50, 2192–2203 (2011). [CrossRef]
J. Dera and D. Stramski, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).
D. A. Toole, D. A. Siegel, D. W. Menzies, M. J. Neumann, and R. C. Smith, “Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability,” Appl. Opt. 39, 456–469 (2000). [CrossRef]
S. B. Hooker and S. Maritorena, “An evaluation of oceanographic radiometers and deployment methodologies,” J. Atmos. Oceanic Technol. 17, 811–830 (2000).
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.
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]
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]
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 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.
Executable code of WASI and manual, ftp://ftp.dfd.dlr.de/pub/WASI .
N. G. Jerlov, Marine Optics (Elsevier, 1976).
W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990). [CrossRef]
F. Kasten and A. T. Young, “Revised optical air mass tables and approximation formula,” Appl. Opt. 28, 4735–4738 (1989). [CrossRef]
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).
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]
R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC, 1995).
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]
T. I. Quickenden and J. A. Irvin, “The ultraviolet absorption spectrum of liquid water,” J. Chem. Phys. 72, 4416–4428 (1980). [CrossRef]
H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994). [CrossRef]
K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. A 64, 1107–1110 (1974). [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.
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.
T. Heege, “Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen am Bodensee,” Ph.D. thesis (DLR-Forschungsbericht, 2000).
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]
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]
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]
R. Doerffer and H. Schiller, “The MERIS Case 2 water algorithm,” Int. J. Remote Sens. 28, 517–535 (2007). [CrossRef]
J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965). [CrossRef]
M. S. Caceci and W. P. Cacheris, “Fitting curves to data,” Byte 9, 340–362 (1984).
C. D. Mobley, Light and Water (Academic, 1994).
C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19, 18927–18944 (2011). [CrossRef]
N. Pinnel, “A method for mapping submerged macrophytes in lakes using hyperspectral remote sensing,” Ph.D. thesis (Technical University Munich, 2007).
P. Gege, “Estimation of phytoplankton concentration from downwelling irradiance measurements in water,” Israel J. Plant Sci. (to be published).

Appl. Opt.

Byte

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

Comput. Geosci.

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]

Comput. J.

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

Int. J. Remote Sens.

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

Israel J. Plant Sci.

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

J. Atmos. Oceanic Technol.

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

J. Chem. Phys.

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

J. Mar. Res.

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

J. Opt. Soc. Am.

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]

J. Opt. Soc. Am. A

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

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]

Limnol. Oceanogr.

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

Oceanologia

J. Dera and D. Stramski, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).
J. Dera and D. Stramski, “Focusing of sunlight by sea surface waves: new results from the Black Sea,” Oceanologia 34, 13–25 (1993).

Opt. Express

C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19, 18927–18944 (2011). [CrossRef]

Proc. SPIE

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

Remote Sens. Environ.

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]

Verh. Internat. Verein. Limnol.

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).

Other

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.
R. E. Walker, Marine Light Field Statistics (Wiley, 1994).
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).
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.
Executable code of WASI and manual, ftp://ftp.dfd.dlr.de/pub/WASI .
N. G. Jerlov, Marine Optics (Elsevier, 1976).
N. Pinnel, “A method for mapping submerged macrophytes in lakes using hyperspectral remote sensing,” Ph.D. thesis (Technical University Munich, 2007).
C. D. Mobley, Light and Water (Academic, 1994).
R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC, 1995).
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.
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.
T. Heege, “Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen am Bodensee,” Ph.D. thesis (DLR-Forschungsbericht, 2000).

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[1] R. E. Walker, Marine Light Field Statistics (Wiley, 1994).

[2] J. R. V. Zanefeld, E. Boss, and A. Barnard, “Influence of surface waves on measured and modeled irradiance profiles,” Appl. Opt. 40, 1442–1449 (2001). [CrossRef]

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

[4] 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).

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

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

[7] D. A. Toole, D. A. Siegel, D. W. Menzies, M. J. Neumann, and R. C. Smith, “Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability,” Appl. Opt. 39, 456–469 (2000). [CrossRef]

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

[9] 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.

[10] 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]

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

[12] 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]

[13] 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]

[14] 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.

[15] Executable code of WASI and manual, ftp://ftp.dfd.dlr.de/pub/WASI .

[16] N. G. Jerlov, Marine Optics (Elsevier, 1976).

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

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

[19] 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).

[20] 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]

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

[22] 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]

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

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

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

[26] 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.

[27] 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.

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

[29] 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]

[30] 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]

[31] 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]

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

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

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

[35] C. D. Mobley, Light and Water (Academic, 1994).

[36] C. D. Mobley, “Fast light calculations for ocean ecosystem and inverse models,” Opt. Express 19, 18927–18944 (2011). [CrossRef]

[37] N. Pinnel, “A method for mapping submerged macrophytes in lakes using hyperspectral remote sensing,” Ph.D. thesis (Technical University Munich, 2007).

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

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Analytic model for the direct and diffuse components of downwelling spectral irradiance in water