Abstract

Subsurface remote sensing signals, represented by the irradiance reflectance and the remote sensing reflectance, were investigated. The present study is based on simulations with the radiative transfer program Hydrolight using optical properties of Lake Constance (German: Bodensee) based on in-situ measurements of the water constituents and the bottom characteristics. Analytical equations are derived for the irradiance reflectance and remote sensing reflectance for deep and shallow water applications. The input of the parameterization are the inherent optical properties of the water-absorption a(λ) and backscattering bb(λ). Additionally, the solar zenith angle θs, the viewing angle θv, and the surface wind speed u are considered. For shallow water applications the bottom albedo RB and the bottom depth zB are included into the parameterizations. The result is a complete set of analytical equations for the remote sensing signals R and Rrs in deep and shallow waters with an accuracy better than 4%. In addition, parameterizations of apparent optical properties were derived for the upward and downward diffuse attenuation coefficients Ku and Kd.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. H.J. Gordon, O.B. Brown, and M.M. Jacobs, �??Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean,�?? Appl. Opt. 14, 417-427 (1975)
    [CrossRef] [PubMed]
  2. L. Prieur, Transfers radiatifs dans les eaux de mer, PhD thesis (Doctorat d�??Etat, Univ. Pierre et Marie Curie, Paris, 1976)
  3. H.R. Gordon and A.Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review (Springer, New York, 1983), Vol. 4.
  4. H.R. Gordon, O.B. Brown, R.H. Evans, J.W. Brown, R.C. Smith, K.S. Baker, and D.K. Clark, �??A semianalytic radiance model of ocean color�??, J. Geoph. Res. 93, 10909-10924 (1988).
    [CrossRef]
  5. 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]
  6. S. Sathyendranath and T. Platt, �??Analytic model of ocean color,�?? Appl. Opt. 36, 2620-2629 (1997).
    [CrossRef] [PubMed]
  7. A.G. Dekker, H.J. Hoogenboom, L.M. Goddijn, and T.J.M. Malthus, �??The relation between inherent optical properties and reflectance spectra in turbid inland waters,�?? Rem. Sens. Rev. 15, 59-74 (1997).
    [CrossRef]
  8. T. Heege, Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen im Bodensee, PhD thesis (Remote Sensing Technology Institute, German Aerospace Center DLR, 2000).
  9. T.T. Bannister, �??Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,�?? Limnol. Oceanogr. 37, 773-780 (1992).
    [CrossRef]
  10. D.R. Lyzenga, �??Passive remote sensing techniques for mapping water depth and bottom features,�?? Appl. Opt. 17, 379-383 (1978).
    [CrossRef] [PubMed]
  11. J. Joseph, �??Untersuchungen ¨uber Ober- und Unterlichtmessungen im Meere und ¨uber ihren Zusammenhang mit Durchsichtigkeitsmessungen,�?? Dt. Hydrogr. Z. 3, 324-335 (1950).
    [CrossRef]
  12. W.D. Philpot and S.G. Ackleson, �??Remote sensing of optically shallow, vertically inhomogeneous waters: a mathematical model�??, Delaware Sea Grant Collage Program (DEL-SG-12-81), 283-299 (1981)
  13. S. Maritorena, A. Morel, and B. Gentili, �??Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo�??, Limnol. Oceanogr. 39, 1689-1703 (1994).
    [CrossRef]
  14. T. Ohde and H. Siegel, �??Correction of bottom influence in ocean colour satellite images of shallow water areas of the Baltic Sea,�?? Int. J. Rem. Sens. 22, 297-313 (2001).
    [CrossRef]
  15. Z. Lee, K.L. Carder, C.D. Mobley, R.G. Steward, and J.S. Patch, �??Hyperspectral remote sensing for shallow waters. 1. A semianalytical model,�?? Appl. Opt. 37, 6329-6338 (1998).
    [CrossRef]
  16. Z. Lee, K.L. Carder, C.D. Mobley, R.G. Steward, and J.S. Patch, �??Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization,�?? Appl. Opt. 38, 3831-3843 (1999).
    [CrossRef]
  17. C.D. Mobley, B. Gentili, H.R. Gordon, Z. Jin, G.W. Kattawar, �?. Morel, P. Reinersman, K. Stamnes, and R.H. Stavn, �??Comparison of numerical models for computing underwater light fields,�?? Appl. Opt. 32, 7484-7504 (1993)
    [CrossRef] [PubMed]
  18. C.D. Mobley, Light and water - radiative transfer in natural waters (Academic Press, San Diego, 1994).
  19. P. Gege, �??Characterization of the phytoplankton in Lake Constance for classification by remote sensing,�?? Arch. Hydrobiol. Adv. Limnol. 53, 179-193 (1998).
  20. H. Buiteveld, J.H.M. Hakvoort, and M. Donze, �??The optical properties of pure water,�?? in Ocean Optics XII, Proc. SPIE 2258, 174-183 (1994).
    [CrossRef]
  21. 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]
  22. P. Gege, Lake Constance: yellow substance measurements in 1998 Technical Report (Remote Sensing Technology Institute for Optoelectronics, German Aerospace Center DLR, 1999).
  23. T.J. Petzold, Volume scattering functions for selected ocean waters (Dowden, Hutchinson & Ross, Stroudsberg, 1977), pp. 152-174.
  24. D. Pozdnyakov, A. Lyaskovsky, H. Grassl, and L. Pettersson, �??Numerical modelling of transspectral processes in natural waters: implications for remote sensing,�?? Int. J. Rem. Sens. 23, 1581-1607 (2002)
    [CrossRef]
  25. S.K. Hawes, K.L. Carder, and G.R. Harvey, �??Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,�?? in Ocean Optics XI, Proc. SPIE 1750, 212-223 (1992).
    [CrossRef]
  26. T. Heege (Remote Sensing Technology Institute, German Aerospace Center DLR, Personal communication, 2003).
  27. K. Bochter and C. Wallh¨au�?er, �??New instrument for simultaneous measurement of the daylight field�??s optical properties above and under water,�?? in Ocean Optics XIII, Proc. SPIE 2963, 631-636 (1997)
    [CrossRef]
  28. W.W. Gregg and K.L. Carder, �??A simple spectral solar irradiance model for cloudless maritime atmospheres,�?? Limnol. Oceanogr. 35, 1657-1675 (1990).
    [CrossRef]
  29. C. Cox and W. Munk, �??Statistics of the sea surface derived from sun glitter,�?? J. Mar. Res. 13, 198-227 (1954).
  30. C. Cox and W. Munk, �??Measurement of the roughness of the sea surface from photographs of the sun�??s glitter,�?? J. Opt. Soc. Am. 44, 838-850 (1954)
    [CrossRef]
  31. 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]
  32. J.T.O. Kirk, �??The upwelling light stream in natural waters,�?? Limnol. Oceanogr. 34, 1410-1425 (1989).
    [CrossRef]

Appl. Opt. (6)

Arch. Hydrobiol. Adv. Limnol. (1)

P. Gege, �??Characterization of the phytoplankton in Lake Constance for classification by remote sensing,�?? Arch. Hydrobiol. Adv. Limnol. 53, 179-193 (1998).

DE Sea Grant Collage Program (1)

W.D. Philpot and S.G. Ackleson, �??Remote sensing of optically shallow, vertically inhomogeneous waters: a mathematical model�??, Delaware Sea Grant Collage Program (DEL-SG-12-81), 283-299 (1981)

Dt. Hydrogr. Z. (1)

J. Joseph, �??Untersuchungen ¨uber Ober- und Unterlichtmessungen im Meere und ¨uber ihren Zusammenhang mit Durchsichtigkeitsmessungen,�?? Dt. Hydrogr. Z. 3, 324-335 (1950).
[CrossRef]

Int. J. Rem. Sens. (2)

T. Ohde and H. Siegel, �??Correction of bottom influence in ocean colour satellite images of shallow water areas of the Baltic Sea,�?? Int. J. Rem. Sens. 22, 297-313 (2001).
[CrossRef]

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, and L. Pettersson, �??Numerical modelling of transspectral processes in natural waters: implications for remote sensing,�?? Int. J. Rem. Sens. 23, 1581-1607 (2002)
[CrossRef]

J. Geoph. Res. (1)

H.R. Gordon, O.B. Brown, R.H. Evans, J.W. Brown, R.C. Smith, K.S. Baker, and D.K. Clark, �??A semianalytic radiance model of ocean color�??, J. Geoph. Res. 93, 10909-10924 (1988).
[CrossRef]

J. Mar. Res. (1)

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. (1)

Limnol. Oceanogr. (7)

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]

J.T.O. Kirk, �??The upwelling light stream in natural waters,�?? Limnol. Oceanogr. 34, 1410-1425 (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]

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]

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]

T.T. Bannister, �??Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,�?? Limnol. Oceanogr. 37, 773-780 (1992).
[CrossRef]

S. Maritorena, A. Morel, and B. Gentili, �??Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo�??, Limnol. Oceanogr. 39, 1689-1703 (1994).
[CrossRef]

Proc. SPIE (3)

H. Buiteveld, J.H.M. Hakvoort, and M. Donze, �??The optical properties of pure water,�?? in Ocean Optics XII, Proc. SPIE 2258, 174-183 (1994).
[CrossRef]

K. Bochter and C. Wallh¨au�?er, �??New instrument for simultaneous measurement of the daylight field�??s optical properties above and under water,�?? in Ocean Optics XIII, Proc. SPIE 2963, 631-636 (1997)
[CrossRef]

S.K. Hawes, K.L. Carder, and G.R. Harvey, �??Quantum fluorescence efficiencies of fulvic and humic acids: effects on ocean color and fluorometric detection,�?? in Ocean Optics XI, Proc. SPIE 1750, 212-223 (1992).
[CrossRef]

Rem. Sens. Rev. (1)

A.G. Dekker, H.J. Hoogenboom, L.M. Goddijn, and T.J.M. Malthus, �??The relation between inherent optical properties and reflectance spectra in turbid inland waters,�?? Rem. Sens. Rev. 15, 59-74 (1997).
[CrossRef]

Other (7)

T. Heege, Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen im Bodensee, PhD thesis (Remote Sensing Technology Institute, German Aerospace Center DLR, 2000).

L. Prieur, Transfers radiatifs dans les eaux de mer, PhD thesis (Doctorat d�??Etat, Univ. Pierre et Marie Curie, Paris, 1976)

H.R. Gordon and A.Y. Morel, Remote assessment of ocean color for interpretation of satellite visible imagery: a review (Springer, New York, 1983), Vol. 4.

C.D. Mobley, Light and water - radiative transfer in natural waters (Academic Press, San Diego, 1994).

T. Heege (Remote Sensing Technology Institute, German Aerospace Center DLR, Personal communication, 2003).

P. Gege, Lake Constance: yellow substance measurements in 1998 Technical Report (Remote Sensing Technology Institute for Optoelectronics, German Aerospace Center DLR, 1999).

T.J. Petzold, Volume scattering functions for selected ocean waters (Dowden, Hutchinson & Ross, Stroudsberg, 1977), pp. 152-174.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1.
Fig. 1.

Distribution of the concentration of suspended matter against phytoplankton for the simulations with Hydrolight.

Fig. 2.
Fig. 2.

Distribution of the concentration values of gelbstoff (top), suspended matter (center), and phytoplankton (bottom) for the simulations with Hydrolight.

Fig. 3.
Fig. 3.

Bottom reflectance spectra used for the forward simulations in Hydrolight.

Fig. 4.
Fig. 4.

Irradiance reflectance for infinitely deep water simulated with Hydrolight (N=22184) depending on x = b b a + b b and the approximation of [1] for a factor f°=0.33 (dashed line).

Fig. 5.
Fig. 5.

Dependence of the irradiance reflectance for infinitely deep water on surface wind (left) and subsurface solar zenith angle (right). The concentrations of the water constituents are CP =3 μg/l, CX =3 mg/l, and aY (λ 0)=0.2m-1.

Fig. 6.
Fig. 6.

Left: irradiance reflectance calculated by Eq. (8) (black crosses) and by the model of [8] (blue points) against the simulated values for infinitely deep water. The 1:1 line is plotted in red. Right: distribution of the relative errors for the approximation of [1] (white bars), [8] (gray bars), and of the new parameterization of Eq. (8) (cross hatched bars).

Fig. 7.
Fig. 7.

Dependence of the remote sensing reflectance for infinitely deep water on the subsurface viewing angle θv . The concentrations of the water constituents are CP =3 μg/l, CX =3 mg/l, and aY (λ 0)=0.2m-1.

Fig. 8.
Fig. 8.

Left: remote sensing reflectance calculated by Eq. (9) against the simulated values for infinitely deep water. The 1:1 line is plotted in red. Right: distribution of the relative errors.

Fig. 9.
Fig. 9.

Downward diffuse attenuation coefficient of 72558 simulations with Hydrolight. Left: dependency on a + b b cos θ s . Right: distribution of the relative errors between calculated and simulated values.

Fig. 10.
Fig. 10.

Dependency of the upward diffuse attenuation coefficient on the sum of absorption and backscattering (left) and subsurface solar zenith angle (right). The points on the left are for θs =8° with colors representing the concentration of suspended matter and the curve on the right is for CP =1 μg/l, CX =1 mg/l, and aY (λ 0)=0.2m-1.

Fig. 11.
Fig. 11.

Irradiance reflectance of shallow water. Comparison of simulated values R 0 and estimated values R (left) with the 1:1 line in red; the green points are the values for wavelengths from 660 to 715 nm. Distribution of the relative error between simulated and estimated irradiance reflectances.

Fig. 12.
Fig. 12.

Irradiance reflectance of shallow water for the spectral range from 400 to 750 nm for three different cases. Left: comparison of simulated (dotted lines) and estimated values (solid lines); right: relative errors. The numbers refer to the following situations: (1) sediment at zB =5 m, CP =10.8 μg/l, CX =50.0 mg/l, aY (440nm)=0.2 m-1, θs =27°, u=1 m/s; (2) macrophytes at zB =6 m, CP =2.5 μg/l, CX =7.0 mg/l, aY (440nm)=0.3 m-1, θs =33°, u=0 m/s; (3) sediment at zB =5 m, CP =1.0 μg/l, CX =1.0 mg/l, aY (440nm)=0.05 m-1, θs =27°, u=1 m/s.

Fig. 13.
Fig. 13.

Remote sensing reflectance of shallow water. Comparison of simulated values R rs,0 and estimated values Rrs (left) with the 1:1 line in red; the green points are the values for wavelengths from 660 to 715 nm. Distribution of the relative error between simulated and estimated remote sensing reflectances.

Fig. 14.
Fig. 14.

Remote sensing reflectance of shallow water for the spectral range from 400 to 750 nm for three different cases and for a subsurface viewing angle of θv =7° on the top and θv =27° on the bottom. The left part shows the comparison of simulated (dotted lines) and estimated values (solid lines) and the right side the relative errors. The numbers refer to the following situations: (1) sediment at zB =5 m, CP =10.8 μg/l, CX =50.0 mg/l, aY (440nm)=0.2 m-1, θs =27°, u=1 m/s; (2) macrophytes at zB =6 m, CP =2.5 μg/l, CX =7.0 mg/l, aY (440nm)=0.3 m-1, θs =33°, u=0 m/s; (3) sediment at zB =5 m, CP =1.0 μg/l, CX =1.0 mg/l, aY (440nm)=0.05 m-1, θs =27°, u=1 m/s.

Tables (4)

Tables Icon

Table 1. Values of the constant factors of phytoplankton and suspended matter for the depth profile in Eq. (7).

Tables Icon

Table 2. Concentrations of the water constituents for the simulations with Hydrolight.

Tables Icon

Table 3. Coefficients for the irradiance reflectance of deep water for Eq. (8) and for the remote sensing reflectance of deep water for Eq. (9).

Tables Icon

Table 4. Coefficients for the irradiance and remote sensing reflectance of Eq. (12) and (13) for shallow water.

Equations (21)

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

R = f b b a + b b f x
R rs , = f b b a + b b f x = f Q x
R = R ( 1 e ( K d + K u , W ) z B ) + R B e ( K d + K u , B ) z B
R rs = R rs , [ 1 exp { ( K d + K u , W cos θ v ) z B } ]
+ R B π exp { ( K d + K u , B cos θ v ) z B }
a ( λ ) = a W ( λ ) + a P ( λ ) + a X ( λ ) + a Y ( λ ) b b ( λ ) = b b , W ( λ ) + b b , P ( λ ) + b b , X ( λ ) + b b , Y ( λ )
a ( λ ) = a W ( λ ) + a P * ( λ ) C P + a Y ( λ 0 ) e S ( λ λ 0 )
b b ( λ ) = 1 2 b W ( λ ) + b b , X * C X
C ( z ) = C 0 + C max exp { 1 2 ( z z max σ ) n }
R = f ( x , θ s , u ) x = f ( x ) f ( θ s ) f ( u ) x
= p 1 ( 1 + p 2 x + p 3 x 2 + p 4 x 3 ) ( 1 + p 5 1 cos θ s ) ( 1 + p 6 u ) x
R rs , = f ( x , θ s , u , θ v ) x = f ( x ) f ( θ s ) f ( u ) f ( θ v ) x
= p 1 ( 1 + p 2 x + p 3 x 2 + p 4 x 3 )
× ( 1 + p 5 1 cos θ s ) ( 1 + p 6 u )
× ( 1 + p 7 1 cos θ v ) x
K d = κ 0 a + b b cos θ s
K u = ( a + b b ) ( 1 + x ) κ 1 ( 1 + κ 2 1 cos θ s )
R = R [ 1 A 1 exp { ( κ 0 cos θ s + ( 1 + x ) κ 1 , W ( 1 + κ 2 , W cos θ s ) ) ( a + b b ) z B } ]
+ A 2 R B exp { ( κ 0 cos θ s + ( 1 + x ) κ 1 , B ( 1 + κ 2 , B cos θ s ) ) ( a + b b ) z B }
R rs = R rs , [ 1 A 1 exp { ( κ 0 cos θ v cos θ s + ( 1 + x ) κ 1 , W ( 1 + κ 2 , W cos θ s ) ) a + b b cos θ v z B } ]
+ A 2 R B π exp { ( κ 0 cos θ v cos θ s + ( 1 + x ) κ 1 , B ( 1 + κ 2 , B cos θ s ) ) a + b b cos θ v z B }

Metrics