Abstract

Lake Victoria, Africa's largest freshwater lake, suffers greatly from negative changes in biomass of species of fish and also from severe eutrophication. The continuing deterioration of Lake Victoria's ecological functions has great long-term consequences for the ecosystem benefits it provides to the countries bordering its shores. However, knowledge about temporal and spatial variations of optical properties and how they relate to lake constituents is important for a number of reasons such as remote sensing, modeling of underwater light fields, and long-term monitoring of lake waters. Based on statistical analysis of data from optical measurements taken during half a year of weekly cruises in Murchison Bay, Lake Victoria, we present a three-component model for the absorption and a two-component model for the scattering of light in the UV and the visible regions of the solar spectrum along with tests of their ranges of validity. The three-component input to the model for absorption is the chlorophyll-a (Chl-a), total suspended materials concentrations, and yellow substance absorption, while the two-component input to the model for scattering is the Chl-a concentration and total suspended materials.

© 2007 Optical Society of America

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References

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  1. M. J. Ntiba, W. M. Kudoja, and C. T. Mukasa, "Management issues in the Lake Victoria watershed," Lakes and Reservoirs: Research and Management 6, 211-216 (2001).
    [CrossRef]
  2. R. Ogutu-Ohwayo, R. E. Hecky, A. S. Cohen, and L. Kaufman, "Human impacts on the African Great, Lakes," Environ. Biol. Fishes 50, 117-131 (1997).
    [CrossRef]
  3. D. K. Branstrator, L. Mwebaza-Ndawula, and J. P. Montoya, "Resource-consumer relationships in Lake Victoria, East Africa," Hydrobiologia 493, 27-34 (2003).
    [CrossRef]
  4. D. Verschuren, T. C. Johnson, H. J. Kling, D. N. Edington, P. R. Leavitt, E. T. Brown, M. R. Talbot, and R. E. Hecky, "History and timing of human impact on Lake Victoria," Proc. R. Soc. London Ser. B 269, 289-294 (2002).
    [CrossRef]
  5. J. H. Wanink and J. J. Kashinde, "Short-term variations in pelagic photosynthesis demand well-timed sampling to monitor long-term limnological changes in Lake Victoria," Hydrobiologia 377, 177-181 (1998).
    [CrossRef]
  6. L. R. Ferber, S. N. Levine, A. Lini, and G. P. Livingston, "Do cyanobacteria dominate in eutrophic lakes because they fix atmospheric nitrogen?"Freshwater Biol. 49, 690-708 (2004).
    [CrossRef]
  7. H. B. O. Lung'ayia, A. M'Harzi, M. Tackx, J. Gichuki, and J. J. Symoens, "Phytoplankton community structure and environment in the Kenyan waters of Lake Victoria," Freshwater Biol. 43, 529-543 (2000).
  8. S. L. Taylor, S. C. Roberts, C. J. Walsh, and B. E. Belinda E. Hatt, "Catchment urbanisation and increased benthic algal biomass in streams: linking mechanisms to management," Freshwater Biol. 49, 835-851 (2004).
    [CrossRef]
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    [CrossRef]
  11. M. Gophen, P. B. O. Ochumba, U. Pollingher, and L. S. Kaufman, "Nile perch (Lates niloticus) invasion in Lake Victoria (East Africa)," Verh. Int. Ver. Limnol. 25, 856-859 (1993).
  12. R. Mugidde, "The increase in phytoplankton primary productivity and biomass in Lake Victoria (Uganda)," Verh. Int. Ver. Limnol. 25, 846-849 (1993).
  13. D. Aksnes and A. Utne, "A revised model of visual range in fish," Sarsia 82, 137-147 (1997).
  14. M. Skogen, E. Svendsen, J. Berntens, D. Aksnes, and K. Ulvertad, "Modelling the primary production in the North-sea using a coupled 3-dimensional physical-chemical-biological ocean model," Estuarine Coastal Shelf Sci. 41, 545-565 (1995).
    [CrossRef]
  15. H. Eilertsen and O. Holm-Hansen, "Effect of high latitude UV radition on phytoplankton and nekton modelled from field measurements by simple algorithms," Adv. Space Res. 19, 173-182 (2000).
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    [CrossRef]
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    [CrossRef]
  28. T. Petzold, "Volume scattering functions for selected ocean waters," SIO Ref. 72-78 (Scripps Institution of Oceanography, 1972).
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    [CrossRef] [PubMed]
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    [CrossRef]
  33. A. Bricaud, A. Morel, M. Babih, K. Allali, and H. Claustre, "Variation in light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
    [CrossRef]
  34. C. Duarte, S. Augusti, and M. Satta, "Partioning particulate light absorption: a budget for a Mediterranean bay," Limnol. Oceanogr. 43, 236-244 (1998).
    [CrossRef]
  35. E. Boss, W. Pegau, W. Gardner, J. Zaneveld, A. Barnard, M. Twardowski, G. Chang, and T. Dickey, "Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf," J. Geophys. Res. 106, 9509-9516 (2001).
    [CrossRef]
  36. A. Morel, Y. Ann, F. Partensky, D. Vaulot, and H. Claustre, "Prochlorococcus and Synechococcus: a comparative study of their optical properties in relation to their size and pigmentation," J. Mar. Res. 51, 617-649 (1993).
    [CrossRef]
  37. J. T. O. Kirk, "Yellow substance (gelbstoff) and its contribution to the attenuation of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 27, 61-71 (1976).
    [CrossRef]
  38. J. T. O. Kirk, "Use of a quanta meter to measure attenuation and underwater reflectance of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 28, 9-21 (1977).
    [CrossRef]
  39. J. T. O. Kirk, "Spectral absorption properties of natural waters: contribution of the soluble and particulate fractions to light absorption in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 31, 287-296 (1980).
    [CrossRef]
  40. P. Bukaveckas and M. Robbins-Forbest, "Role of dissolved organic carbon in the attenuation of photosynthetically active radiation in Adirondack lakes," Freshwater Biol. 43, 339-354 (2000).
    [CrossRef]
  41. J. T. O. Kirk, Light and Photosynethesis in Aquatic Ecosystem (Cambrigde, 1994).
    [CrossRef]
  42. J. F. Talling, "Generalized and specialized features of phytoplankton as a form of photosynthetic cover," in Prediction and Measurement of Photosynthetic Productivity (Wageningen: Pudoc, 1970), pp. 431-445.
  43. S. W. Effler, R. K. Gelda, J. A. Bloomfield, S. O. Quinn, and D. L. Johnson, "Modeling the effects of tripton on water clarity: Lake Champlain," J. Water Resour. Plan. Manage. 127, 224-234 (2001).
    [CrossRef]

2004 (2)

L. R. Ferber, S. N. Levine, A. Lini, and G. P. Livingston, "Do cyanobacteria dominate in eutrophic lakes because they fix atmospheric nitrogen?"Freshwater Biol. 49, 690-708 (2004).
[CrossRef]

S. L. Taylor, S. C. Roberts, C. J. Walsh, and B. E. Belinda E. Hatt, "Catchment urbanisation and increased benthic algal biomass in streams: linking mechanisms to management," Freshwater Biol. 49, 835-851 (2004).
[CrossRef]

2003 (2)

2002 (1)

D. Verschuren, T. C. Johnson, H. J. Kling, D. N. Edington, P. R. Leavitt, E. T. Brown, M. R. Talbot, and R. E. Hecky, "History and timing of human impact on Lake Victoria," Proc. R. Soc. London Ser. B 269, 289-294 (2002).
[CrossRef]

2001 (6)

M. J. Ntiba, W. M. Kudoja, and C. T. Mukasa, "Management issues in the Lake Victoria watershed," Lakes and Reservoirs: Research and Management 6, 211-216 (2001).
[CrossRef]

Ø. Frette, S. Erga, J. J. Stamnes, and K. Stamnes, "Optical remote sensing of waters with vertical structure," Appl. Opt. 40, 1478-1487 (2001).
[CrossRef]

E. Boss, W. Pegau, W. Gardner, J. Zaneveld, A. Barnard, M. Twardowski, G. Chang, and T. Dickey, "Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf," J. Geophys. Res. 106, 9509-9516 (2001).
[CrossRef]

S. W. Effler, R. K. Gelda, J. A. Bloomfield, S. O. Quinn, and D. L. Johnson, "Modeling the effects of tripton on water clarity: Lake Champlain," J. Water Resour. Plan. Manage. 127, 224-234 (2001).
[CrossRef]

J. Piskozub, P. Flatau, and J. Zaneveld, "Monte Carlo study of the scattering error of a quartz reflective absorption tube," J. Atmos. Ocean. Technol. 18, 438-445 (2001).
[CrossRef]

E. H. S. Van-Duin, G. Blom, F. J. Los, R. Maffione, C. F. Zimmerman, R. Cerco, M. Dortch, and E. P. H. Best, "Modeling underwater light climate in relation to sedimentation, resuspension, water quality and autotrophic growth," Hydrobiologia 444, 25-42 (2001).
[CrossRef]

2000 (3)

P. Bukaveckas and M. Robbins-Forbest, "Role of dissolved organic carbon in the attenuation of photosynthetically active radiation in Adirondack lakes," Freshwater Biol. 43, 339-354 (2000).
[CrossRef]

H. B. O. Lung'ayia, A. M'Harzi, M. Tackx, J. Gichuki, and J. J. Symoens, "Phytoplankton community structure and environment in the Kenyan waters of Lake Victoria," Freshwater Biol. 43, 529-543 (2000).

H. Eilertsen and O. Holm-Hansen, "Effect of high latitude UV radition on phytoplankton and nekton modelled from field measurements by simple algorithms," Adv. Space Res. 19, 173-182 (2000).

1998 (4)

A. Bricaud, A. Morel, M. Babih, K. Allali, and H. Claustre, "Variation in light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

C. Duarte, S. Augusti, and M. Satta, "Partioning particulate light absorption: a budget for a Mediterranean bay," Limnol. Oceanogr. 43, 236-244 (1998).
[CrossRef]

J. H. Wanink and J. J. Kashinde, "Short-term variations in pelagic photosynthesis demand well-timed sampling to monitor long-term limnological changes in Lake Victoria," Hydrobiologia 377, 177-181 (1998).
[CrossRef]

Ø. Frette, J. J. Stamnes, and K. Stamnes, "Optical remote sensing of marine constituents in coastal waters: a feasibility study," Appl. Opt. 37, 8318-8326 (1998).
[CrossRef]

1997 (2)

R. Ogutu-Ohwayo, R. E. Hecky, A. S. Cohen, and L. Kaufman, "Human impacts on the African Great, Lakes," Environ. Biol. Fishes 50, 117-131 (1997).
[CrossRef]

D. Aksnes and A. Utne, "A revised model of visual range in fish," Sarsia 82, 137-147 (1997).

1995 (1)

M. Skogen, E. Svendsen, J. Berntens, D. Aksnes, and K. Ulvertad, "Modelling the primary production in the North-sea using a coupled 3-dimensional physical-chemical-biological ocean model," Estuarine Coastal Shelf Sci. 41, 545-565 (1995).
[CrossRef]

1994 (1)

1993 (4)

A. Morel, Y. Ann, F. Partensky, D. Vaulot, and H. Claustre, "Prochlorococcus and Synechococcus: a comparative study of their optical properties in relation to their size and pigmentation," J. Mar. Res. 51, 617-649 (1993).
[CrossRef]

M. Gophen, P. B. O. Ochumba, U. Pollingher, and L. S. Kaufman, "Nile perch (Lates niloticus) invasion in Lake Victoria (East Africa)," Verh. Int. Ver. Limnol. 25, 856-859 (1993).

R. Mugidde, "The increase in phytoplankton primary productivity and biomass in Lake Victoria (Uganda)," Verh. Int. Ver. Limnol. 25, 846-849 (1993).

R. E. Hecky, "The eutrophication of Lake Victoria," Verh. Int. Ver. Limnol. 25, 39-48 (1993).

1989 (1)

P. B. O. Ochumba and D. I. Kibaara, "Observations on blue-green algal blooms in the open waters of Lake Victoria, Kenya," Afr. J. Ecol. 27, 23-34 (1989).
[CrossRef]

1987 (1)

J. Fischer and R. Deorffer, "An inverse technique for remote detection of suspended matter, phytoplankton and yellow substance from CZCS measurements," Polar Res. 7, 21-26 (1987).

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)

J. T. O. Kirk, "Spectral absorption properties of natural waters: contribution of the soluble and particulate fractions to light absorption in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 31, 287-296 (1980).
[CrossRef]

1977 (1)

J. T. O. Kirk, "Use of a quanta meter to measure attenuation and underwater reflectance of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 28, 9-21 (1977).
[CrossRef]

1976 (1)

J. T. O. Kirk, "Yellow substance (gelbstoff) and its contribution to the attenuation of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 27, 61-71 (1976).
[CrossRef]

Adv. Space Res. (1)

H. Eilertsen and O. Holm-Hansen, "Effect of high latitude UV radition on phytoplankton and nekton modelled from field measurements by simple algorithms," Adv. Space Res. 19, 173-182 (2000).

Afr. J. Ecol. (1)

P. B. O. Ochumba and D. I. Kibaara, "Observations on blue-green algal blooms in the open waters of Lake Victoria, Kenya," Afr. J. Ecol. 27, 23-34 (1989).
[CrossRef]

Appl. Opt. (4)

Aus. J. Mar. Freshwater Res. (3)

J. T. O. Kirk, "Yellow substance (gelbstoff) and its contribution to the attenuation of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 27, 61-71 (1976).
[CrossRef]

J. T. O. Kirk, "Use of a quanta meter to measure attenuation and underwater reflectance of photosynthetically active radiation in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 28, 9-21 (1977).
[CrossRef]

J. T. O. Kirk, "Spectral absorption properties of natural waters: contribution of the soluble and particulate fractions to light absorption in some inland and coastal Southeastern Australian waters," Aus. J. Mar. Freshwater Res. 31, 287-296 (1980).
[CrossRef]

Environ. Biol. Fishes (1)

R. Ogutu-Ohwayo, R. E. Hecky, A. S. Cohen, and L. Kaufman, "Human impacts on the African Great, Lakes," Environ. Biol. Fishes 50, 117-131 (1997).
[CrossRef]

Estuarine Coastal Shelf Sci. (1)

M. Skogen, E. Svendsen, J. Berntens, D. Aksnes, and K. Ulvertad, "Modelling the primary production in the North-sea using a coupled 3-dimensional physical-chemical-biological ocean model," Estuarine Coastal Shelf Sci. 41, 545-565 (1995).
[CrossRef]

Freshwater Biol. (4)

P. Bukaveckas and M. Robbins-Forbest, "Role of dissolved organic carbon in the attenuation of photosynthetically active radiation in Adirondack lakes," Freshwater Biol. 43, 339-354 (2000).
[CrossRef]

L. R. Ferber, S. N. Levine, A. Lini, and G. P. Livingston, "Do cyanobacteria dominate in eutrophic lakes because they fix atmospheric nitrogen?"Freshwater Biol. 49, 690-708 (2004).
[CrossRef]

H. B. O. Lung'ayia, A. M'Harzi, M. Tackx, J. Gichuki, and J. J. Symoens, "Phytoplankton community structure and environment in the Kenyan waters of Lake Victoria," Freshwater Biol. 43, 529-543 (2000).

S. L. Taylor, S. C. Roberts, C. J. Walsh, and B. E. Belinda E. Hatt, "Catchment urbanisation and increased benthic algal biomass in streams: linking mechanisms to management," Freshwater Biol. 49, 835-851 (2004).
[CrossRef]

Hydrobiologia (3)

D. K. Branstrator, L. Mwebaza-Ndawula, and J. P. Montoya, "Resource-consumer relationships in Lake Victoria, East Africa," Hydrobiologia 493, 27-34 (2003).
[CrossRef]

J. H. Wanink and J. J. Kashinde, "Short-term variations in pelagic photosynthesis demand well-timed sampling to monitor long-term limnological changes in Lake Victoria," Hydrobiologia 377, 177-181 (1998).
[CrossRef]

E. H. S. Van-Duin, G. Blom, F. J. Los, R. Maffione, C. F. Zimmerman, R. Cerco, M. Dortch, and E. P. H. Best, "Modeling underwater light climate in relation to sedimentation, resuspension, water quality and autotrophic growth," Hydrobiologia 444, 25-42 (2001).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

J. Piskozub, P. Flatau, and J. Zaneveld, "Monte Carlo study of the scattering error of a quartz reflective absorption tube," J. Atmos. Ocean. Technol. 18, 438-445 (2001).
[CrossRef]

J. Geophys. Res. (2)

E. Boss, W. Pegau, W. Gardner, J. Zaneveld, A. Barnard, M. Twardowski, G. Chang, and T. Dickey, "Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf," J. Geophys. Res. 106, 9509-9516 (2001).
[CrossRef]

A. Bricaud, A. Morel, M. Babih, K. Allali, and H. Claustre, "Variation in light absorption by suspended particles with chlorophyll a concentration in oceanic (case 1) waters: analysis and implications for bio-optical models," J. Geophys. Res. 103, 31033-31044 (1998).
[CrossRef]

J. Mar. Res. (1)

A. Morel, Y. Ann, F. Partensky, D. Vaulot, and H. Claustre, "Prochlorococcus and Synechococcus: a comparative study of their optical properties in relation to their size and pigmentation," J. Mar. Res. 51, 617-649 (1993).
[CrossRef]

J. Water Resour. Plan. Manage. (1)

S. W. Effler, R. K. Gelda, J. A. Bloomfield, S. O. Quinn, and D. L. Johnson, "Modeling the effects of tripton on water clarity: Lake Champlain," J. Water Resour. Plan. Manage. 127, 224-234 (2001).
[CrossRef]

Lakes and Reservoirs: Research and Management (1)

M. J. Ntiba, W. M. Kudoja, and C. T. Mukasa, "Management issues in the Lake Victoria watershed," Lakes and Reservoirs: Research and Management 6, 211-216 (2001).
[CrossRef]

Limnol. Oceanogr. (2)

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]

C. Duarte, S. Augusti, and M. Satta, "Partioning particulate light absorption: a budget for a Mediterranean bay," Limnol. Oceanogr. 43, 236-244 (1998).
[CrossRef]

Polar Res. (1)

J. Fischer and R. Deorffer, "An inverse technique for remote detection of suspended matter, phytoplankton and yellow substance from CZCS measurements," Polar Res. 7, 21-26 (1987).

Proc. R. Soc. London (1)

D. Verschuren, T. C. Johnson, H. J. Kling, D. N. Edington, P. R. Leavitt, E. T. Brown, M. R. Talbot, and R. E. Hecky, "History and timing of human impact on Lake Victoria," Proc. R. Soc. London Ser. B 269, 289-294 (2002).
[CrossRef]

Sarsia (1)

D. Aksnes and A. Utne, "A revised model of visual range in fish," Sarsia 82, 137-147 (1997).

Verh. Int. Ver. Limnol. (3)

M. Gophen, P. B. O. Ochumba, U. Pollingher, and L. S. Kaufman, "Nile perch (Lates niloticus) invasion in Lake Victoria (East Africa)," Verh. Int. Ver. Limnol. 25, 856-859 (1993).

R. Mugidde, "The increase in phytoplankton primary productivity and biomass in Lake Victoria (Uganda)," Verh. Int. Ver. Limnol. 25, 846-849 (1993).

R. E. Hecky, "The eutrophication of Lake Victoria," Verh. Int. Ver. Limnol. 25, 39-48 (1993).

Other (11)

S. W. Jeffrey, R. F. Mantoura, and S. W. Wright, "Phytoplankton pigments in oceanography," in Monographs on Oceanographic Methodology (SCOR/UNESCO, 1997), Vol. 10.

R. Doerffer, "Protocols for the validation of MERIS water products," ESA Doc. PO-TN-MEL-GS-0043, GKSS (European Space Agency, 2002).

N. Jerlov, Optical Oceanography (Elsevier, 1968).

W. H. Flaig, B. C. R. Beutelspacher, and R. Reitz, "Chemical composition and physical properties of humic substances," in Soil Components: Organic Compounds, J. E. Gieseking, ed. (Springer, 1975), Vol. 1, pp. 1-21.

E. T. Gjessing, Physical and Chemical Characteristics of Aquatic Humus (Ann Arbor Science, 1976).

J. T. O. Kirk, Light and Photosynthesis in Aquatic Ecosystems (Cambridge, 1983).

G. K. Bhattacharya and R. A. Johnson, Statistical Concepts and Methods (Wiley, 1977).

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).

J. T. O. Kirk, Light and Photosynethesis in Aquatic Ecosystem (Cambrigde, 1994).
[CrossRef]

J. F. Talling, "Generalized and specialized features of phytoplankton as a form of photosynthetic cover," in Prediction and Measurement of Photosynthetic Productivity (Wageningen: Pudoc, 1970), pp. 431-445.

T. Petzold, "Volume scattering functions for selected ocean waters," SIO Ref. 72-78 (Scripps Institution of Oceanography, 1972).

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Figures (5)

Fig. 1
Fig. 1

Map showing the measurement stations in Murchison Bay, Lake Victoria (Uganda).

Fig. 2
Fig. 2

Regression coefficients for absorption (upper part) and scattering (lower part); see Eqs. (6) and (7).

Fig. 3
Fig. 3

Profiles of measured absorption and calculated scattering coefficients at the nine channels of the ac-9 instrument from station 5. The wavelengths of the channels are 412, 440, 488, 510, 532, 555, 650, 676, and 715   nm , as indicated by the code shown in the upper part of the figure. The constant value of absorption coefficient at a wavelength of 715   nm comes from the use of this channel as a baseline correction (procedure described in Section 2). The measured scattering coefficients are obtained from measured absorption and attenuation coefficients by use of Eq. (1).

Fig. 4
Fig. 4

Surface absorption (upper part) and scattering (lower part) coefficients in Murchison Bay, Lake Victoria for all cruises at stations 3, 4, 5, and 6. The dashed-dotted curves are extrapolated and the solid curves are measured.

Fig. 5
Fig. 5

Mean values of measured (solid curves) and extrapolated (dashed-dotted) surface absorption coefficients (upper part) and the measured surface values of the absorption coefficients of yellow substance (lower part) in Lake Victoria for all cruises at stations 3, 4, 5, and 6.

Tables (4)

Tables Icon

Table 1 Locations of Measurement Stations in Murchison Bay

Tables Icon

Table 2 Chlorophyll- a and Total Suspended Material Concentrations Retrieved From Filtration of Water Samples From Murchison Bay, Lake Victoria

Tables Icon

Table 3 Model for the Absorption Coefficient in the UV and Visible Regions [cf. Eq. (6)]

Tables Icon

Table 4 Model for the Scattering Coefficient in the UV and Visible Regions [cf. Eq. (7)]

Equations (14)

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

b = c a .
a ( λ ) = a w ( λ ) + a y ( λ ) + a alg ( λ ) + a inor ( λ ) ,
a y ( λ ) = a ( λ 0 ) e γ ( λ λ 0 ) ,
b ( λ ) = b w ( λ ) + b a lg ( λ ) + b i n o r ( λ ) ,
M a lg = p M C ,
a ( λ ) = a w ( λ ) + a y ( λ ) + α 1 ( λ ) p M C + α 2 ( λ ) × ( M T S M p M C ) ,
b ( λ ) = b w ( λ ) + β 1 ( λ ) p M C + β 2 ( λ ) × ( M T S M p M C ) ,
b ( λ ) = b ( λ o ) ( λ o λ ) n ,
y = α 1 x 1 + α 2 x 2 ,
R 2 = α 1 S x 1 y + α 2 S x 2 y S y 2 ,
S x 1 y = i = 1 n ( x i 1 x ¯ 1 ) ( y i y ¯ ) ,
S x 2 y = i = 1 n ( x i 2 x ¯ 2 ) ( y i y ¯ ) ,
S y 2 = i = 1 n ( y i y ¯ ) 2
y = β 1 x 1 + β 2 x 2 ,

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