Abstract

We use remote sensing reflectance (RSR) together with the inherent optical properties of suspended particulates to determine the backscattering ratio bb/b for coastal waters. We examine the wavelength dependence of bb(λ) and f(λ)/Q(λ) and establish the conditions when C(λ) in RSR(λ) ≅ C(λ)bb(λ)/a(λ) can be treated as a constant. We found that for case 2 waters, RSR was insensitive to the natural fluctuations in particle-size distributions. The cross-sectional area of the suspended particulate per unit volume, xg, showed an excellent correlation with the volume scattering coefficient.

© 1997 Optical Society of America

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References

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  1. K. L. Carder, S. K. Hawes, Z. P. Lee, “SEAWIFS algorithm for chlorophyll a and dissolved organic matter in a subtropical environment,” J. Geophys. Res. (to be published).
  2. A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
    [CrossRef] [PubMed]
  3. O. Ulloa, S. Sathyendranath, T. Platt, “Effects of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
    [CrossRef] [PubMed]
  4. R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
    [CrossRef]
  5. W. D. Phillpot, “Radiative transfer in stratified waters: a single-scattering approximation for irradiance,” Appl. Opt. 26, 4123–4132 (1987).
    [CrossRef]
  6. H. R. Gordon, O. B. Brown, “Irradiance reflectivity of a flat ocean as a function of its optical properties,” Appl. Opt. 12, 1549–1551 (1973); H. R. Gordon, O. B. Brown, M. Jacobs, “Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
    [CrossRef] [PubMed]
  7. A. Y. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
    [CrossRef]
  8. J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
    [CrossRef]
  9. J. H. Jerome, R. P. Bukata, J. E. Burton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988).
    [CrossRef] [PubMed]
  10. A. Y. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991); “Diffuse reflectance of oceanic waters: bi-directional aspects,” 32, 6864–6879 (1993).
  11. M. Sydor, R. A. Arnone, R. A. Gould, “Remote sensing reflectance of Case 2 waters,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 222–227 (1997).
    [CrossRef]
  12. S. Tassan, “Local algorithms using SeaWiFS data for the retrieval of phytoplankton, pigments, suspended sediment, and yellow substance in coastal waters,” Appl. Opt. 33, 2369–2378 (1994).
    [CrossRef] [PubMed]
  13. R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
    [CrossRef]
  14. D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
    [CrossRef]

1996

1994

1991

1988

1987

1984

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

1980

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

1977

A. Y. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

1973

Arnone, R. A.

R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
[CrossRef]

M. Sydor, R. A. Arnone, R. A. Gould, “Remote sensing reflectance of Case 2 waters,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 222–227 (1997).
[CrossRef]

Brown, O. B.

Bukata, R. P.

Burton, J. E.

Carder, K. L.

K. L. Carder, S. K. Hawes, Z. P. Lee, “SEAWIFS algorithm for chlorophyll a and dissolved organic matter in a subtropical environment,” J. Geophys. Res. (to be published).

Gedney, R. T.

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

Gentili, B.

Gordon, H. R.

Gould, R. A.

M. Sydor, R. A. Arnone, R. A. Gould, “Remote sensing reflectance of Case 2 waters,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 222–227 (1997).
[CrossRef]

Gould, R. W.

R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
[CrossRef]

Hawes, S. K.

K. L. Carder, S. K. Hawes, Z. P. Lee, “SEAWIFS algorithm for chlorophyll a and dissolved organic matter in a subtropical environment,” J. Geophys. Res. (to be published).

Jerome, J. H.

Kirk, J. T. O.

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

Lee, Z. P.

K. L. Carder, S. K. Hawes, Z. P. Lee, “SEAWIFS algorithm for chlorophyll a and dissolved organic matter in a subtropical environment,” J. Geophys. Res. (to be published).

Morel, A.

Morel, A. Y.

Oriol, R. A.

R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
[CrossRef]

Pennock, J. R.

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Phillpot, W. D.

Platt, T.

Prieur, L.

A. Y. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

Salzman, J.

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

Sathyendranath, S.

Shook, D. F.

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

Stumpf, R. P.

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Svehla, R. A.

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

Sydor, M.

M. Sydor, R. A. Arnone, R. A. Gould, “Remote sensing reflectance of Case 2 waters,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 222–227 (1997).
[CrossRef]

Tassan, S.

Terrie, G.

R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
[CrossRef]

Ulloa, O.

Appl. Opt.

W. D. Phillpot, “Radiative transfer in stratified waters: a single-scattering approximation for irradiance,” Appl. Opt. 26, 4123–4132 (1987).
[CrossRef]

H. R. Gordon, O. B. Brown, “Irradiance reflectivity of a flat ocean as a function of its optical properties,” Appl. Opt. 12, 1549–1551 (1973); H. R. Gordon, O. B. Brown, M. Jacobs, “Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean,” Appl. Opt. 14, 417–427 (1975).
[CrossRef] [PubMed]

A. Morel, B. Gentili, “Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem,” Appl. Opt. 35, 4850–4862 (1996).
[CrossRef] [PubMed]

O. Ulloa, S. Sathyendranath, T. Platt, “Effects of the particle-size distribution on the backscattering ratio in seawater,” Appl. Opt. 33, 7070–7077 (1994).
[CrossRef] [PubMed]

J. H. Jerome, R. P. Bukata, J. E. Burton, “Utilizing the components of vector irradiance to estimate the scalar irradiance in natural waters,” Appl. Opt. 27, 4012–4018 (1988).
[CrossRef] [PubMed]

A. Y. Morel, B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30, 4427–4438 (1991); “Diffuse reflectance of oceanic waters: bi-directional aspects,” 32, 6864–6879 (1993).

S. Tassan, “Local algorithms using SeaWiFS data for the retrieval of phytoplankton, pigments, suspended sediment, and yellow substance in coastal waters,” Appl. Opt. 33, 2369–2378 (1994).
[CrossRef] [PubMed]

J. Geophys. Res.

D. F. Shook, J. Salzman, R. A. Svehla, R. T. Gedney, “Quantitative interpretation of Great Lakes remote sensing data,” J. Geophys. Res. 85, 3991–3996 (1980).
[CrossRef]

Limnol. Oceanogr.

A. Y. Morel, L. Prieur, “Analysis of variations in ocean color,” Limnol. Oceanogr. 22, 709–722 (1977).
[CrossRef]

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr. 29, 350–356 (1984).
[CrossRef]

Remote Sens. Environ.

R. P. Stumpf, J. R. Pennock, “Remote estimation of the diffuse attenuation coefficient in a moderately turbid estuary,” Remote Sens. Environ. 38, 183–191 (1991).
[CrossRef]

Other

M. Sydor, R. A. Arnone, R. A. Gould, “Remote sensing reflectance of Case 2 waters,” in Ocean Optics XIII, S. G. Ackleson, ed., Proc. SPIE2963, 222–227 (1997).
[CrossRef]

K. L. Carder, S. K. Hawes, Z. P. Lee, “SEAWIFS algorithm for chlorophyll a and dissolved organic matter in a subtropical environment,” J. Geophys. Res. (to be published).

R. A. Arnone, R. W. Gould, R. A. Oriol, G. Terrie, “Effects of vertical chlorophyll structure and solar irradiance on remote sensing ocean color spectrum,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 322–331 (1994).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Particle-size distribution in St. Louis Bay has a slightly bimodal shape with an inflection at 2.5 µm. The mean particle diameter ranged from 1.8 to 2.1 µm. The dotted curves represent the resolution of particle sizes into two component distributions.

Fig. 2
Fig. 2

Particle-size distribution, which is seen to behave according to ln(n × 10-9) = -0.51x + 3.9, is typical of coastal waters.

Fig. 3
Fig. 3

Plots of b(λ) reveal an ∼1/λ dependence with wavelength.

Fig. 4
Fig. 4

Main contribution to xg comes from the 2–5-µm particles.

Fig. 5
Fig. 5

xg and b correlate with r2 > 0.9. The linear relationship appears to hold for three geographical areas: Camp Lejeune (Camp Les.), N.C., the Gulf of Mexico, and St. Louis Bay, Miss.

Fig. 6
Fig. 6

a(λ) has an exponential behavior for λ < 600 nm: curve 1, a(λ) for the Jourdan River station (high DOM, ∼2-g/m3 suspended solids); curve 2, a(λ) at the mouth of St. Louis Bay, lower DOM, ∼10-g/m3 suspended solids. The Gulf of Mexico stations are shown by curves 3 and 4. Curve 4 can be considered typical of the relatively clear seawater having a Secchi transparency of 3 m.

Fig. 7
Fig. 7

RSR at 660 nm at constant a shows a linear relationship with xg for six St. Louis Bay stations independent of the suspended solids concentration and the inherent fluctuations in particle-size distribution from station to station.

Fig. 8
Fig. 8

RSR versus b/a is also linear at λ = 660 nm according to RSR = 0.00062b/a. The linear relationship breaks down for λ < 650 nm because C becomes a function of turbidity.

Fig. 9
Fig. 9

For case 2 waters, Kd(λ) and Ku(λ) are nearly the same and RSR is linear with b/Kd for all λ independent of DOM. RSR = Ckb/Kd, where Ck is the slope. Curve 1, the Mississippi Sound low DOM, ∼3 g/m3; curve 2, Jourdan River, high DOM, 2 g/m3.

Fig. 10
Fig. 10

Spectral dependence of bb(λ) derived from the measurements of RSR(λ) and Kd(λ): curve 1, a station with ∼10-g/m3 suspended load; dotted line, curve 2, 0.0125b(λ) for the same station; curve 3, bb(λ) for the Mississippi Sound; curve 4, bb(λ) for the Jourdan River.

Fig. 11
Fig. 11

Spectral dependence of f(λ)/Q(λ) for the Jourdan River, curve 1 and for the Mississippi Sound, curve 2. f/Q is reasonably flat in the 450–620-nm range but deviates markedly from the accepted value in the long wavelength region. The dotted line shows a nominal value of f/Q ∼ 0.094 used in satellite remote sensing of turbid water.

Fig. 12
Fig. 12

Area-wide average of RSR(λ) versus xg/a(λ) for 1 km2 (representative of case 2 pixel with an average suspended load of ∼4 g/m3). RSR(λ) falls along a distinct loop of points depending on λ, as marked. The slopes of the dashed lines correspond to C in the range 0.046 < C < 0.063. The accepted value of C is 0.054. For St. Louis Bay bb ∼ 0.15xg.

Fig. 13
Fig. 13

RSR(λ) versus b/a for two stations: curve 1, Jourdan River station (∼2 g/m3, high DOM); curve 2, St. Louis Bay (5 g/m3, lower DOM).

Fig. 14
Fig. 14

RSR versus xg/a regardless of λ. The dotted line represents a linear region where C is a constant (the slope of the line for xg/a < 0.6 corresponds to C ∼ 0.055). The solid line gives a second-order polynomial fit according to RSR = 0.0093(xg/a)–0.0018(xg/a)2. The nonlinear region, xg/a > 0.6, indicates the onset of multiple scattering and corresponds to bb/a > 0.09.

Equations (9)

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Rfbb/a.
RSRλ=Cλbbλ/aλ
RSRλ0.051bbλ/aλ,
RλBbλ/Kdλ+Kuλ.
RλBbλ/2Kdλ.
5°20°02πσpθ, ϕ, λsin θdθdϕ=2π5°20°σrθ, λsin θdθ,
xg=i=130nriπri2,
CbRSRλKdλ=bbλ.
CbRSR/2RBbCbΔΩLwθ, φcosθdΩ02πdφ0π/22Lwθ, φcosθsinθdθBb.

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