Abstract

The downwelling irradiance in water is highly variable due to the focusing and defocusing of sunlight and skylight by the wave-modulated water surface. While the time scales and intensity variations caused by wave focusing are well studied, little is known about the induced spectral variability. Also, the impact of variations of sensor depth and inclination during the measurement on spectral irradiance has not been studied much. We have developed a model that relates the variance of spectral irradiance to the relevant parameters of the environmental and experimental conditions. A dataset from three German lakes was used to validate the model and to study the importance of each effect as a function of depth for the range of 0 to 5m.

© 2011 Optical Society of America

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References

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  1. R. E. Walker, Marine Light Field Statistics (Wiley, 1994).
  2. J. R. V. Zaneveld, 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, “Maximum effects of sunlight focusing under a wind-disturbed sea surface,” Oceanologia 23, 15–42 (1986).
  4. J. Dera and D. Stramski, “Focusing of sunlight by sea surface waves: new results from the Black Sea,” Oceanologia 34, 13–25 (1993).
  5. V. L. Weber, “Coefficient of variation of underwater irradiance fluctuations,” Radiophys. Quantum Electron. 53, 13–27 (2010).
    [CrossRef]
  6. 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]
  7. M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
    [CrossRef]
  8. 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).
  9. H. Siegel and H.-J. Brosin, “Regional differences in the spectral reflectance of sea water,” Beiträge zur Meereskunde 55, 71–77 (1986).
  10. J.-M. Froidefond and S. Ouillon, “Introducing a mini-catamaran to perform reflectance measurements above and below the water surface,” Opt. Express 13, 926–936(2005).
    [CrossRef] [PubMed]
  11. P. Gege is preparing a manuscript to be called “Analytic model for the direct and diffuse components of downwelling spectral irradiance in water.”
  12. W. W. Gregg and K. L. Carder, “A simple spectral solar irradiance model for cloudless maritime atmospheres,” Limnol. Oceanogr. 35, 1657–1675 (1990).
    [CrossRef]
  13. R. Bukata, J. H. Jerome, K. Y. Kondratyev, and D. V. Pozdnyakov, Optical Properties and Remote Sensing of Inland and Coastal Waters (CRC Press, 1995).
  14. 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]
  15. C. D. Mobley, Light and Water (Academic, 1994).
  16. T. I. Quickenden and J. A. Irvin, “The ultraviolet absorption spectrum of liquid water,” J. Chem. Phys. 72, 4416–4428(1980).
    [CrossRef]
  17. H. Buiteveld, J. H. M. Hakvoort, and M. Donze, “The optical properties of pure water,” Proc. SPIE 2258, 174–183(1994).
    [CrossRef]
  18. K. F. Palmer and D. Williams, “Optical properties of water in the near infrared,” J. Opt. Soc. Am. 64, 1107–1110 (1974).
    [CrossRef]
  19. A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N.G.Jerlov, E.Steemann Nielsen, eds. (Academic, 1997), pp. 1–24.
  20. 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, U.Gaedke, eds. (Archiv für Hydriobiologie, 1998), Vol.  53, pp. 179–193.
  21. T. Heege, “Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen am Bodensee,” Ph.D. thesis (DLR-Forschungsbericht, 2000).
  22. 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]
  23. 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]
  24. J. L. Mueller and R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, S.B.Hooker, E.R.Firestone, and J.G.Acker, eds., Tech. memo 104566 (NASA, 1995), Vol.  25.
  25. G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8, 252–258 (2006).
    [CrossRef]
  26. 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]
  27. 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.
    [CrossRef]
  28. The R Foundation for Statistical Computing, “R version 2.11.1,” http://www.r-project.org/.

2010 (1)

V. L. Weber, “Coefficient of variation of underwater irradiance fluctuations,” Radiophys. Quantum Electron. 53, 13–27 (2010).
[CrossRef]

2008 (1)

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).

2006 (2)

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8, 252–258 (2006).
[CrossRef]

2005 (1)

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 (1)

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 (1)

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

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 (2)

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 (2)

H. Siegel and H.-J. Brosin, “Regional differences in the spectral reflectance of sea water,” Beiträge zur Meereskunde 55, 71–77 (1986).

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

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)

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.
[CrossRef]

Austin, R. W.

J. L. Mueller and R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, S.B.Hooker, E.R.Firestone, and J.G.Acker, eds., Tech. memo 104566 (NASA, 1995), Vol.  25.

Barnard, A.

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]

Brosin, H.-J.

H. Siegel and H.-J. Brosin, “Regional differences in the spectral reflectance of sea water,” Beiträge zur Meereskunde 55, 71–77 (1986).

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 Press, 1995).

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]

Darecki, M.

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8, 252–258 (2006).
[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).

Donze, M.

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

Emanuel, N.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

Froidefond, J.-M.

Gege, P.

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 is preparing a manuscript to be called “Analytic model for the direct and diffuse components of downwelling spectral irradiance in water.”

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, U.Gaedke, eds. (Archiv für Hydriobiologie, 1998), Vol.  53, 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.
[CrossRef]

Gordon, H. R.

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]

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]

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]

Hauschild, M.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[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).

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]

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 Press, 1995).

Keck, J.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

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 Press, 1995).

Lawson, M.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

Leavitt, B.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

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).

Menzies, D. W.

Mobley, C. D.

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

Morel, 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]

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

Mueller, J. L.

J. L. Mueller and R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, S.B.Hooker, E.R.Firestone, and J.G.Acker, eds., Tech. memo 104566 (NASA, 1995), Vol.  25.

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]

Ouillon, S.

Palmer, K. F.

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).

Perk, R.

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

Pozdnyakov, D. V.

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

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).
[CrossRef]

Quickenden, T. I.

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

Siegel, D. A.

Siegel, H.

H. Siegel and H.-J. Brosin, “Regional differences in the spectral reflectance of sea water,” Beiträge zur Meereskunde 55, 71–77 (1986).

Smith, R. C.

Stramski, D.

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).

Toole, D. A.

Walker, R. E.

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

Weber, V. L.

V. L. Weber, “Coefficient of variation of underwater irradiance fluctuations,” Radiophys. Quantum Electron. 53, 13–27 (2010).
[CrossRef]

Williams, D.

Zaneveld, J. R. V.

Zibordi, G.

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8, 252–258 (2006).
[CrossRef]

Appl. Opt. (2)

Beiträge zur Meereskunde (1)

H. Siegel and H.-J. Brosin, “Regional differences in the spectral reflectance of sea water,” Beiträge zur Meereskunde 55, 71–77 (1986).

Comput. Geosci. (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]

GISci. Remote Sens. (1)

M. Lawson, B. Leavitt, N. Emanuel, R. Perk, J. Keck, and M. Hauschild, “Compensating for irradiance fluxes when measuring the spectral reflectance of corals in situ,” GISci. Remote Sens. 43, 111–127 (2006).
[CrossRef]

J. Chem. Phys. (1)

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

J. Opt. A: Pure Appl. Opt. (1)

G. Zibordi and M. Darecki, “Immersion factors for the RAMSES series of hyper-spectral underwater radiometers,” J. Opt. A: Pure Appl. Opt. 8, 252–258 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

Limnol. Oceanogr. (4)

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 (2)

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 (1)

Proc. SPIE (1)

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

Radiophys. Quantum Electron. (1)

V. L. Weber, “Coefficient of variation of underwater irradiance fluctuations,” Radiophys. Quantum Electron. 53, 13–27 (2010).
[CrossRef]

Verh. Internat. Verein. Limnol. (1)

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 (10)

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

P. Gege is preparing a manuscript to be called “Analytic model for the direct and diffuse components of downwelling spectral irradiance in water.”

A. Morel, “Optical properties of pure water and pure sea water,” in Optical Aspects of Oceanography, N.G.Jerlov, 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, U.Gaedke, eds. (Archiv für Hydriobiologie, 1998), Vol.  53, pp. 179–193.

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

J. L. Mueller and R. W. Austin, “Ocean optics protocols for SeaWiFS validation, revision 1,” SeaWiFS Technical Report Series, S.B.Hooker, E.R.Firestone, and J.G.Acker, eds., Tech. memo 104566 (NASA, 1995), Vol.  25.

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

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.
[CrossRef]

The R Foundation for Statistical Computing, “R version 2.11.1,” http://www.r-project.org/.

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

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Figures (11)

Fig. 1
Fig. 1

Sensor depth and inclination of all individual data takes.

Fig. 2
Fig. 2

Environmental and experimental factors responsible for irradiance variance: 1, variance of direct irradiance due to wave focusing; 2, variance induced by tilting sensor (scaled by a factor of 250); 3, variance of diffuse irradiance due to wave focusing; 4, variance of sensor depth.

Fig. 3
Fig. 3

Dependency of the ratio of direct to diffuse irradiance on (a) Sun zenith angle and (b) depth.

Fig. 4
Fig. 4

Illustration of the geometry factor.

Fig. 5
Fig. 5

Example for the variability of irradiance measurements caused mainly by wave focusing and changing sensor tilt.

Fig. 6
Fig. 6

Example for the variability of irradiance measurements caused mainly by sensor depth variation.

Fig. 7
Fig. 7

Dominating components of irradiance variance. Proportions of variance: 1 = 85.5 % , 2 = 6.2 % , 3 = 4.7 % , 4 = 1.6 % .

Fig. 8
Fig. 8

Intensity variability of irradiance as a function of depth: (a) relative differences of a single spectra and (b) variances during a measurement.

Fig. 9
Fig. 9

Relationship between (a) irradiance intensity variability and the changes of direct component and (b) sensor depth for selected depth intervals.

Fig. 10
Fig. 10

Examples for spectral variability during a measurement: (a) RE17, relative irradiance changes caused mainly by wave focusing and changing sensor tilt and (b) 20_1, caused mainly by depth variation.

Fig. 11
Fig. 11

Spectral variability of irradiance as function of depth: (a) relative spectral changes across the visible (400 versus 700 nm ) and (b) in the near infrared (755 versus 700 nm ).

Tables (3)

Tables Icon

Table 1 Model Parameters and Values Used for Simulation

Tables Icon

Table 2 Depth Dependency of Intensity Variability and Correlation with Main Causes a

Tables Icon

Table 3 Depth Dependency of Indices Describing Spectral Variability of Irradiance and Correlation with Parameters Describing the Main Causes a

Equations (21)

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 s ( z ) = E d s ( 0 ) exp { K d s z l d s } .
E d d ( z ) = E d d ( 0 ) exp { K d d z cos θ Sun } ·
d E d ( z ) = d f d d E d d ( z ) + f d d d E d d ( z ) + d f d s E d s ( z ) + f d s d E d s ( z ) .
d E d d ( z ) = [ d E d d ( 0 ) E d d ( 0 ) K d d cos θ Sun d z ] exp { K d d z cos θ Sun } .
E d d ( 0 ) = E d d 0 cos ( θ Sun + θ s ) ,
d E d d ( 0 ) = E d d 0 sin ( θ Sun + θ s ) d θ s = E d d ( 0 ) tan ( θ Sun + θ s ) d θ s ,
d E d d ( z ) = E d d ( z ) [ tan ( θ Sun + θ s ) d θ s + K d d cos θ Sun d z ] .
d E d s ( z ) = K d s E d s ( z ) l d s d z .
r d ( z ) = f d d E d d ( z ) f d s E d s ( z ) ,
E d d ( z ) = r d ( z ) r d ( z ) + 1 E d ( z ) f d d ,
E d s ( z ) = 1 r d ( z ) + 1 E d ( z ) f d s .
d E d ( z ) = E d ( z ) r d ( z ) r d ( z ) + 1 [ tan ( θ Sun + θ s ) d θ s + K d d cos θ Sun d z d f d d f d d ] E d ( z ) r d ( z ) + 1 [ K d s l d s d z d f d s f d s ] .
d E d ( z ) E d ( z ) = r d ( z ) r d ( z ) + 1 d f d d f d d r d ( z ) r d ( z ) + 1 tan ( θ Sun + θ s ) d θ s 1 r d ( z ) + 1 [ K d d r d ( z ) cos θ Sun + l d s K d s ] d z + 1 r d ( z ) + 1 d f d s f d s .
var [ Δ E d ( λ , z ) E d ( λ , z ) ] = [ r d ( λ , z ) r d ( λ , z ) + 1 ] 2 var [ Δ f d d f d d ] + [ r d ( λ , z ) r d ( λ , z ) + 1 ] 2 tan 2 ( θ Sun + θ s ) var [ θ s ] + [ 1 r d ( λ , z ) + 1 ] 2 [ K d d ( λ ) r d ( λ , z ) cos θ Sun + l d s K d s ( λ ) ] 2 var [ z ] + [ 1 r d ( λ , z ) + 1 ] 2 var [ Δ f d s f d s ] .
r d ( 0 ) = f d d f d s 2 T r T a s ( 1 ρ d d ) [ 1 T r 0.95 + 2 T r 1.5 ( 1 T a s ) F a ] ( 1 ρ d s ) .
r d ( z ) = r d ( 0 ) exp { ( l d s K d s K d d cos θ Sun ) z } .
K d s ( λ ) = K d d ( λ ) = a ( λ ) + b b ( λ ) ,
a ( λ ) = a W ( λ ) + C a p h * ( λ ) + Y exp [ S ( λ 440 ) ] ,
b b ( λ ) = b b , W ( λ ) + X b b , X * .
γ VIS , i = E d , i ( 400 ) E d ( 400 ) E d , i ( 700 ) E d ( 700 ) , γ NIR , i = E d , i ( 755 ) E d ( 755 ) E d , i ( 700 ) E d ( 700 ) .

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