Abstract

Ratio processing methods are reviewed, and a new method is proposed for extracting water depth and bottom type information from passive multispectral scanner data. Limitations of each technique are discussed, and an error analysis is performed using an analytical model for the radiance over shallow water.

© 1978 Optical Society of America

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References

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  1. F. C. Polcyn, W. L. Brown, I. J. Sattinger, “The Measurement of Water Depth by Remote Sensing Techniques,” Report 8973-26-F, Willow Run Laboratories, The University of Michigan, Ann Arbor (1970).
  2. C. T. Wezernak, D. R. Lyzenga, Remote Sensing Environ. 4, 37 (1975).
    [CrossRef]
  3. F. C. Polcyn, D. R. Lyzenga, “Calculation of Water Depth from ERTS—MSS Data,” in Proceedings Symposium on Significant Results Obtained from ERTS-1, NASA Publication SP-327 (1973).
  4. D. Lyzenga, F. Thomson, “Data Processing and Evaluation for Panama City Coastal Survey: Bathymetry Results,” Report 121400-1-T, Environmental Research Institute of Michigan, Ann Arbor, Mich. (1976).
  5. N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).
  6. T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Visibility Laboratory Tech. Report 72-78, Scripps Institution of Oceanography, San Diego, Calif. (1972).
  7. J. L. Mueller, Appl. Opt. 15, 394 (1976).
    [CrossRef] [PubMed]
  8. W. R. McCluney, Remote Sensing Environ. 5, 3 (1976).
    [CrossRef]
  9. W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).
  10. L. Elterman, “UV, Visible and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, Air Force Cambridge Research Laboratories, Bedford, Mass. (1970).
  11. H. R. Gordon, Appl. Opt. 12, 2803 (1973).
    [CrossRef] [PubMed]
  12. W. R. McCluney, “Estimation of Sunlight Penetration in the Sea for Remote Sensing,” NASA Report TM X-70643 (1974).
  13. D. R. Lyzenga, Appl. Opt. 16, 282 (1977).
    [CrossRef] [PubMed]
  14. The use of K instead of c* = (1 − w0F)c in the quasi-single-scattering approximation represents a further approximation, which is valid if K is measured under direct solar illumination with the sun near zenith, see H. R. Gordon, J. Opt. Soc. Am. 64, 773 (1974).
    [CrossRef]
  15. H. R. Gordon, O. B. Brown, Appl. Opt. 13, 2153 (1974).
    [CrossRef] [PubMed]

1977

1976

J. L. Mueller, Appl. Opt. 15, 394 (1976).
[CrossRef] [PubMed]

W. R. McCluney, Remote Sensing Environ. 5, 3 (1976).
[CrossRef]

1975

C. T. Wezernak, D. R. Lyzenga, Remote Sensing Environ. 4, 37 (1975).
[CrossRef]

1974

1973

Brown, O. B.

Brown, W. L.

F. C. Polcyn, W. L. Brown, I. J. Sattinger, “The Measurement of Water Depth by Remote Sensing Techniques,” Report 8973-26-F, Willow Run Laboratories, The University of Michigan, Ann Arbor (1970).

Crane, R. B.

W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).

Elterman, L.

L. Elterman, “UV, Visible and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, Air Force Cambridge Research Laboratories, Bedford, Mass. (1970).

Gordon, H. R.

Jerlov, N. G.

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).

Lyzenga, D.

D. Lyzenga, F. Thomson, “Data Processing and Evaluation for Panama City Coastal Survey: Bathymetry Results,” Report 121400-1-T, Environmental Research Institute of Michigan, Ann Arbor, Mich. (1976).

Lyzenga, D. R.

D. R. Lyzenga, Appl. Opt. 16, 282 (1977).
[CrossRef] [PubMed]

C. T. Wezernak, D. R. Lyzenga, Remote Sensing Environ. 4, 37 (1975).
[CrossRef]

F. C. Polcyn, D. R. Lyzenga, “Calculation of Water Depth from ERTS—MSS Data,” in Proceedings Symposium on Significant Results Obtained from ERTS-1, NASA Publication SP-327 (1973).

Malila, W. A.

W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).

McCluney, W. R.

W. R. McCluney, Remote Sensing Environ. 5, 3 (1976).
[CrossRef]

W. R. McCluney, “Estimation of Sunlight Penetration in the Sea for Remote Sensing,” NASA Report TM X-70643 (1974).

Mueller, J. L.

Omarzu, C. A.

W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).

Petzold, T. J.

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Visibility Laboratory Tech. Report 72-78, Scripps Institution of Oceanography, San Diego, Calif. (1972).

Polcyn, F. C.

F. C. Polcyn, W. L. Brown, I. J. Sattinger, “The Measurement of Water Depth by Remote Sensing Techniques,” Report 8973-26-F, Willow Run Laboratories, The University of Michigan, Ann Arbor (1970).

F. C. Polcyn, D. R. Lyzenga, “Calculation of Water Depth from ERTS—MSS Data,” in Proceedings Symposium on Significant Results Obtained from ERTS-1, NASA Publication SP-327 (1973).

Sattinger, I. J.

F. C. Polcyn, W. L. Brown, I. J. Sattinger, “The Measurement of Water Depth by Remote Sensing Techniques,” Report 8973-26-F, Willow Run Laboratories, The University of Michigan, Ann Arbor (1970).

Thomson, F.

D. Lyzenga, F. Thomson, “Data Processing and Evaluation for Panama City Coastal Survey: Bathymetry Results,” Report 121400-1-T, Environmental Research Institute of Michigan, Ann Arbor, Mich. (1976).

Turner, R. E.

W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).

Wezernak, C. T.

C. T. Wezernak, D. R. Lyzenga, Remote Sensing Environ. 4, 37 (1975).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Remote Sensing Environ.

W. R. McCluney, Remote Sensing Environ. 5, 3 (1976).
[CrossRef]

C. T. Wezernak, D. R. Lyzenga, Remote Sensing Environ. 4, 37 (1975).
[CrossRef]

Other

F. C. Polcyn, D. R. Lyzenga, “Calculation of Water Depth from ERTS—MSS Data,” in Proceedings Symposium on Significant Results Obtained from ERTS-1, NASA Publication SP-327 (1973).

D. Lyzenga, F. Thomson, “Data Processing and Evaluation for Panama City Coastal Survey: Bathymetry Results,” Report 121400-1-T, Environmental Research Institute of Michigan, Ann Arbor, Mich. (1976).

N. G. Jerlov, Optical Oceanography (Elsevier, New York, 1968).

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” Visibility Laboratory Tech. Report 72-78, Scripps Institution of Oceanography, San Diego, Calif. (1972).

W. A. Malila, R. B. Crane, C. A. Omarzu, R. E. Turner, Studies of Spectral Discrimination, Report 31650-22-T, Willow Run Laboratories, University of Michigan, Ann Arbor (1971).

L. Elterman, “UV, Visible and IR Attenuation for Altitudes to 50 km,” Report AFCRL-68-0153, Air Force Cambridge Research Laboratories, Bedford, Mass. (1970).

W. R. McCluney, “Estimation of Sunlight Penetration in the Sea for Remote Sensing,” NASA Report TM X-70643 (1974).

F. C. Polcyn, W. L. Brown, I. J. Sattinger, “The Measurement of Water Depth by Remote Sensing Techniques,” Report 8973-26-F, Willow Run Laboratories, The University of Michigan, Ann Arbor (1970).

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Figures (4)

Fig. 1
Fig. 1

Plot of X1 vs X2 for water type 3 with three bottom types. Water depth ranges from 0 m to 5 m on each curve.

Fig. 2
Fig. 2

Spectral reflectances of sand, mud, and green vegetation.

Fig. 3
Fig. 3

Total probability of misclassification for three bottom types in water type 3, using the proposed method.

Fig. 4
Fig. 4

Total depth error using the proposed method and depth error due to noise using the ratio method for water and bottom types shown in Fig. 1.

Equations (28)

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L i = L si + k i r Bi exp ( κ i fz ) ,
r A 1 r A 2 = r B 1 r B 2 = . . . = R b ,
z = 1 ( κ 1 κ 2 ) f [ ln ( k 1 k 2 ) ln ( R R b ) ] ,
R = ( L 1 L s 1 ) / ( L 2 L s 2 ) .
R = ( k 1 r B 1 ) / ( k 2 r B 2 ) ,
r B = r B π β ( μ s ) K ( μ + μ ) .
X i = ln ( L i L si ) ,
Y i = j = 1 N A ij X j
Y N = B m Cz ,
Y m 1 < Y 1 < Y m 2 ,
P ( m , n ) = ½ erf ( d 1 2 ) ½ erf ( d 2 2 ) ,
d 1 = ( Y ̂ m Y n 1 ) / σ m ,
d 2 = ( Y ̂ m Y n 2 ) / σ m ,
σ m 2 = i = 1 2 A 1 i 2 ( NE Δ L i ) 2 / ( L ̂ i L si ) 2 .
P ̅ ( m ) = 1 P ( m , m ) .
( Δ Y N ) 2 = i = 1 N A Ni 2 ( NE Δ L i ) 2 / ( L ̂ i L si ) 2
Δ Z m = 1 C [ ( Δ Y N ) 2 + n P ( m , n ) ( B m B n ) 2 ] 1 / 2 .
Δ Z r = 1 ( κ 1 κ 2 ) f [ ( NE Δ L 1 L 1 L s 1 ) 2 + ( NE Δ L 2 L 2 L s 2 ) 2 ] 1 / 2 .
L ( μ , ϕ ) = E 0 S ( μ , μ 0 , ϕ ) + 0 1 0 2 π L ( μ , ϕ ) S ( μ , μ , ϕ ) μ d μ d ϕ 1 0 1 0 2 π R ( μ ) S ( μ , μ , ϕ ) μ d μ d ϕ ,
S ( μ , μ , ϕ ) = 1 K ( μ + μ ) 1 { 1 exp [ ( 1 μ + 1 μ ) Kz ] } β ( μ s ) + r B π exp [ ( 1 μ + 1 μ ) Kz ] ,
μ s = μ μ + [ ( 1 μ 2 ) ( 1 μ 2 ) ] 1 / 2 cos ϕ .
X ̂ i = a i b i z
A Nj = b j ( k = 1 N b k 2 ) 1 / 2 .
k = 1 N A ik A jk = { 0 , i j 1 , i = j
det ( A ij ) = 1 .
A ij = b i + 1 b j ( k = 1 i b k 2 ) 1 / 2 ( k = 1 i + 1 b k 2 ) 1 / 2 for j = 1 . . . i ,
A ij = ( k = 1 i b k 2 ) 1 / 2 ( k = 1 i + 1 b k 2 ) 1 / 2 for j = i + 1 ,
A ij = 0 for j = i + 2 . . . N .

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