Abstract

What we believe to be a new inversion procedure for multi- and hyperspectral data in shallow water, represented by the subsurface irradiance and remote sensing reflectance spectra, was developed based on analytical equations by using the method of nonlinear curve fitting. The iteration starts using an automatic determination of the initial values of the fit parameters: concentration of phytoplankton and suspended matter, absorption of gelbstoff, bottom depth, and the fractions of up to six bottom types. Initial values of the bottom depth and suspended matter concentration are estimated analytically. Phytoplankton concentration and gelbstoff absorption are initially calculated by the method of nested intervals. A sensitivity analysis was made to estimate the accuracy of the entire inversion procedure including model error, error propagation, and influence of instrument characteristics such as noise, and radiometric and spectral resolution. The entire inversion technique is included in a public-domain software (WASI) to provide a fast and user-friendly tool of forward and inverse modeling.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. J. Kirk, Monte Carlo procedure for simulating the penetration of light into natural waters, CSIRO Division of Plant Industry, Technical Paper 36, 1-16 (1981).
  4. R. Preisendorfer, Hydrologic Optics (U.S. Department of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Pacific Marine Environmental Laboratory, 1976).
  5. C. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).
  14. P. Gege, "Characterization of the phytoplankton in Lake Constance for classification by remote sensing," Arch. Hydrobiol. Spec. Issues Adv. Limnol. 53, 179-193 (1998).
  15. T. Heege, "Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen im Bodensee," Ph.D. thesis (Institut für Methodik der Fernerkundung, Deutsches Zentrum für Luft- und Raumfahrt Oberpfaffenhofen, 2000).
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    [CrossRef] [PubMed]
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  18. P. Gege and A. Albert, in Remote Sensing of Aquatic Coastal Ecosystem Processes, Vol. 9 of Remote Sensing and Digital Image Processing, L. L. Richardson and E. F. LeDrew, eds. (Springer, 2006), Chap. 4.
  19. J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).
  20. M. Caceci and W. Cacheris, "Fitting curves to data--the simplex algorithm is the answer," Byte Mag. 9(5), 340-362 (1984).
  21. P. Gege, "The water colour simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra," Comput. Geosci. 30, 523-532 (2004).
    [CrossRef]
  22. M. Babin and D. Stramski, "Light absorption by aquatic particles in the near-infrared spectral region," Limnol. Oceanogr. 47, 911-915 (2002).
    [CrossRef]
  23. 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]
  24. P. Gege, "Error propagation at inversion of irradiance reflectance spectra in case-2 waters," in Ocean Optics XVI, Santa Fe, N. Mex., 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).
  25. J. Schulz, "Systemtechnische Untersuchungen an dem abbildenden Spektrometer ROSIS-01 zur Erfassung und Interpretation der Meeresfarbe," Ph.D. dissertation (Institut für Optoelektronik, Deutsche Forschungsanstalt für Luft- und Raumfahrt Oberpfaffenhofen, 1997).
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  28. J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).
  29. D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
    [PubMed]

2004 (1)

P. Gege, "The water colour simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra," Comput. Geosci. 30, 523-532 (2004).
[CrossRef]

2003 (1)

2002 (2)

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

M. Babin and D. Stramski, "Light absorption by aquatic particles in the near-infrared spectral region," Limnol. Oceanogr. 47, 911-915 (2002).
[CrossRef]

2001 (1)

F. Fell and J. Fischer, "Numerical simulation of the light field in the atmosphere-ocean system using the matrix-operator method," J. Quant. Spectrosc. Radiat. Transfer 69, 351-388 (2001).
[CrossRef]

1999 (2)

1998 (1)

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

1995 (1)

1994 (1)

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]

1993 (1)

H. Krawczyk, A. Neumann, T. Walzel, and G. Zimmermann, "Investigation of interpretation possibilities of spectral high-dimensional measurements by means of principle component analysis: a concept for physical interpretation of those measurements," in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, Jr. and R. A. Schowengerdt, eds., Proc. SPIE 1938, 401-411 (1993).
[CrossRef]

1984 (2)

M. Caceci and W. Cacheris, "Fitting curves to data--the simplex algorithm is the answer," Byte Mag. 9(5), 340-362 (1984).

J. Fischer and H. Grassl, "Radiative transfer in an atmosphere-ocean system: an azimuthally dependent matrix-operator approach," Appl. Opt. 23, 1032-1039 (1984).
[CrossRef] [PubMed]

1981 (1)

J. Kirk, Monte Carlo procedure for simulating the penetration of light into natural waters, CSIRO Division of Plant Industry, Technical Paper 36, 1-16 (1981).

1977 (1)

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
[CrossRef]

1973 (1)

1965 (1)

J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Albert, A.

A. Albert and C. Mobley, "An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters," Opt. Express 11, 2873-2890 (2003).
[CrossRef] [PubMed]

A. Albert, "Inversion technique for optical remote sensing in shallow water," Ph.D. dissertation (University of Hamburg, Department of Earth Sciences, 2004), http://www.sub.uni-hamburg.de/opus/volltexte/2005/2325/.

P. Gege and A. Albert, in Remote Sensing of Aquatic Coastal Ecosystem Processes, Vol. 9 of Remote Sensing and Digital Image Processing, L. L. Richardson and E. F. LeDrew, eds. (Springer, 2006), Chap. 4.

Babin, M.

M. Babin and D. Stramski, "Light absorption by aquatic particles in the near-infrared spectral region," Limnol. Oceanogr. 47, 911-915 (2002).
[CrossRef]

Bissett, W.

C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

Brown, O.

Bulgarelli, B.

Caceci, M.

M. Caceci and W. Cacheris, "Fitting curves to data--the simplex algorithm is the answer," Byte Mag. 9(5), 340-362 (1984).

Cacheris, W.

M. Caceci and W. Cacheris, "Fitting curves to data--the simplex algorithm is the answer," Byte Mag. 9(5), 340-362 (1984).

Carder, K.

Chavez, F.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Cota, G.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Cunningham, A.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Davis, C.

C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

Doerffer, R.

R. Doerffer and H. Schiller, "Determination of case 2 water constituents using radiative transfer simulation and its inversion by neural network," in Proceedings of Ocean Optics XIV Conference, Hawaii, November 10-13, S. G. Ackleson, ed. (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 1998).

Fell, F.

F. Fell and J. Fischer, "Numerical simulation of the light field in the atmosphere-ocean system using the matrix-operator method," J. Quant. Spectrosc. Radiat. Transfer 69, 351-388 (2001).
[CrossRef]

Fischer, J.

F. Fell and J. Fischer, "Numerical simulation of the light field in the atmosphere-ocean system using the matrix-operator method," J. Quant. Spectrosc. Radiat. Transfer 69, 351-388 (2001).
[CrossRef]

J. Fischer and H. Grassl, "Radiative transfer in an atmosphere-ocean system: an azimuthally dependent matrix-operator approach," Appl. Opt. 23, 1032-1039 (1984).
[CrossRef] [PubMed]

Gege, P.

P. Gege, "The water colour simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra," Comput. Geosci. 30, 523-532 (2004).
[CrossRef]

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

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

P. Gege and A. Albert, in Remote Sensing of Aquatic Coastal Ecosystem Processes, Vol. 9 of Remote Sensing and Digital Image Processing, L. L. Richardson and E. F. LeDrew, eds. (Springer, 2006), Chap. 4.

P. Gege, "Error propagation at inversion of irradiance reflectance spectra in case-2 waters," in Ocean Optics XVI, Santa Fe, N. Mex., 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

P. Gege, "Gaussian model for yellow substance absorption spectra," in Ocean Optics XV, Monaco, France, 16-20 October, 2000, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2000).

Gentili, B.

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]

Gordon, H.

Grassl, H.

J. Fischer and H. Grassl, "Radiative transfer in an atmosphere-ocean system: an azimuthally dependent matrix-operator approach," Appl. Opt. 23, 1032-1039 (1984).
[CrossRef] [PubMed]

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
[PubMed]

Heege, T.

T. Heege, "Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen im Bodensee," Ph.D. thesis (Institut für Methodik der Fernerkundung, Deutsches Zentrum für Luft- und Raumfahrt Oberpfaffenhofen, 2000).

Kaczmarek, S.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Kahru, M.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Kirk, J.

J. Kirk, Monte Carlo procedure for simulating the penetration of light into natural waters, CSIRO Division of Plant Industry, Technical Paper 36, 1-16 (1981).

Kishino, M.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Kisselev, V.

Kowalczuk, P.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Krawczyk, H.

H. Krawczyk, A. Neumann, T. Walzel, and G. Zimmermann, "Investigation of interpretation possibilities of spectral high-dimensional measurements by means of principle component analysis: a concept for physical interpretation of those measurements," in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, Jr. and R. A. Schowengerdt, eds., Proc. SPIE 1938, 401-411 (1993).
[CrossRef]

Lee, Z.

Lyaskovsky, A.

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
[PubMed]

Maritorena, S.

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]

McKee, D.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Mead, R.

J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Mitchell, B.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Mobley, C.

A. Albert and C. Mobley, "An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters," Opt. Express 11, 2873-2890 (2003).
[CrossRef] [PubMed]

Z. Lee, K. Carder, C. Mobley, R. Steward, and J. Patch, "Hyperspectral remote sensing for shallow waters: 2. Deriving bottom depths and water properties by optimization," Appl. Opt. 38, 3831-3843 (1999).
[CrossRef]

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

C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

Montes, M.

C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

Morel, A.

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]

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
[CrossRef]

Nelder, J.

J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

Neumann, A.

H. Krawczyk, A. Neumann, T. Walzel, and G. Zimmermann, "Investigation of interpretation possibilities of spectral high-dimensional measurements by means of principle component analysis: a concept for physical interpretation of those measurements," in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, Jr. and R. A. Schowengerdt, eds., Proc. SPIE 1938, 401-411 (1993).
[CrossRef]

Patch, J.

Perona, G.

Pettersson, L.

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
[PubMed]

Phinney, D.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Pozdnyakov, D.

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
[PubMed]

Preisendorfer, R.

R. Preisendorfer, Hydrologic Optics (U.S. Department of Commerce, National Oceanic and Atmospheric Administration, Environmental Research Laboratories, Pacific Marine Environmental Laboratory, 1976).

Prieur, L.

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
[CrossRef]

Raine, R.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Roberti, L.

Schiller, H.

R. Doerffer and H. Schiller, "Determination of case 2 water constituents using radiative transfer simulation and its inversion by neural network," in Proceedings of Ocean Optics XIV Conference, Hawaii, November 10-13, S. G. Ackleson, ed. (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 1998).

Schulz, J.

J. Schulz, "Systemtechnische Untersuchungen an dem abbildenden Spektrometer ROSIS-01 zur Erfassung und Interpretation der Meeresfarbe," Ph.D. dissertation (Institut für Optoelektronik, Deutsche Forschungsanstalt für Luft- und Raumfahrt Oberpfaffenhofen, 1997).

Schwarz, J.

J. Schwarz, P. Kowalczuk, S. Kaczmarek, G. Cota, B. Mitchell, M. Kahru, F. Chavez, A. Cunningham, D. McKee, P. Gege, M. Kishino, D. Phinney, and R. Raine, "Two models for absorption by colored dissolved organic matter (CDOM)," Oceanologia 44, 209-241 (2002).

Steward, R.

Stramski, D.

M. Babin and D. Stramski, "Light absorption by aquatic particles in the near-infrared spectral region," Limnol. Oceanogr. 47, 911-915 (2002).
[CrossRef]

Sundman, L.

C. Mobley, L. Sundman, C. Davis, M. Montes, and W. Bissett, "A look-up-table approach to inverting remotely sensed ocean color data," in Ocean Optics XVI, Santa Fe, USA, 18-22 November, 2002, Proceedings on CD (U.S. Office of Naval Research, Ocean, Atmosphere, and Space Science and Technology Department, 2002).

Tanis, F.

D. Pozdnyakov, A. Lyaskovsky, H. Grassl, L. Pettersson, and F. Tanis, "Optically shallow waters: modeling of radiometric colour and development of water quality retrieval algorithms," in Seventh International Conference on Remote Sensing for Marine and Coastal Environments, Miami, Fla., 20-22 May, 2002, Proceedings on CD (Veridian Systems Division, 2002).
[PubMed]

Walzel, T.

H. Krawczyk, A. Neumann, T. Walzel, and G. Zimmermann, "Investigation of interpretation possibilities of spectral high-dimensional measurements by means of principle component analysis: a concept for physical interpretation of those measurements," in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, Jr. and R. A. Schowengerdt, eds., Proc. SPIE 1938, 401-411 (1993).
[CrossRef]

Zimmermann, G.

H. Krawczyk, A. Neumann, T. Walzel, and G. Zimmermann, "Investigation of interpretation possibilities of spectral high-dimensional measurements by means of principle component analysis: a concept for physical interpretation of those measurements," in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, Jr. and R. A. Schowengerdt, eds., Proc. SPIE 1938, 401-411 (1993).
[CrossRef]

Appl. Opt. (5)

Arch. Hydrobiol. (1)

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

Byte (1)

M. Caceci and W. Cacheris, "Fitting curves to data--the simplex algorithm is the answer," Byte Mag. 9(5), 340-362 (1984).

Comput. Geosci. (1)

P. Gege, "The water colour simulator WASI: an integrating software tool for analysis and simulation of optical in situ spectra," Comput. Geosci. 30, 523-532 (2004).
[CrossRef]

Comput. J. (1)

J. Nelder and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).

J. Quant. Spectrosc. Radiat. Transfer (1)

F. Fell and J. Fischer, "Numerical simulation of the light field in the atmosphere-ocean system using the matrix-operator method," J. Quant. Spectrosc. Radiat. Transfer 69, 351-388 (2001).
[CrossRef]

Limnol. Oceanogr. (3)

A. Morel and L. Prieur, "Analysis of variations in ocean color," Limnol. Oceanogr. 22, 709-722 (1977).
[CrossRef]

M. Babin and D. Stramski, "Light absorption by aquatic particles in the near-infrared spectral region," Limnol. Oceanogr. 47, 911-915 (2002).
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Figures (10)

Fig. 1
Fig. 1

Variability of the factor f° of Eq. (6). The thick curves represent the average values for the given concentration of suspended matter and for 0.5 C P 20.0 µg ∕l and 0.1 a Y ( λ 0 ) 5.0 m - 1 . The thin curves are the mean plus and minus one standard deviation.

Fig. 2
Fig. 2

Bottom depth estimated by Eq. (9) for varying concentrations of 0.5 C P 20.0 µg l , 0.5 C X 10.0 mg l , and 0.1 a Y ( λ 0 ) 5.0 m - 1 above sediment and macrophytes. The bottom albedo is assumed to be known during the calculations. Solid curves: mean; dashed curves: intervals given by the standard deviation.

Fig. 3
Fig. 3

Relative error of the bottom depth estimated using Eq. (9) depending on the concentration of suspended matter (top) and the relative error of C X (bottom) above macrophytes: C P = 2 µg l and a Y ( 440 nm ) = 0.3 m - 1 . The dependence on the relative error of C X was calculated for C X = 2 mg /l . The subsurface solar zenith angle was 30°.

Fig. 4
Fig. 4

Relative error of the estimated phytoplankton concentration (top) and gelbstoff absorption (bottom) using nested intervals and the Simplex algorithm depending on the relative error of the bottom depth above macrophytes; if not varied, the values were fixed at C P = 2 µg ∕l , C X = 2 µg l , a Y ( 440 nm ) = 0.3 m - 1 , and z B = 3 m . The subsurface solar zenith angle was 30°.

Fig. 5
Fig. 5

Relative error of suspended matter (top) and phytoplankton (bottom) concentration resulting from the inversion of the Hydrolight simulated spectra of the irradiance reflectance for different values of the bottom depth above sediment. If not varied, C P = 2 µg l , C X = 2 mg l , and a Y ( 440 nm ) = 0.3 m - 1 was set.

Fig. 6
Fig. 6

Relative error of retrieved bottom depth using the Hydrolight spectra of the remote sensing reflectance depending on phytoplankton (top) and suspended matter concentration (bottom) above sediment. If not varied, C P = 2 µg /l , C X = 2 mg /l , and a Y ( 440 nm ) = 0.3 m - 1 was set.

Fig. 7
Fig. 7

Relative error of gelbstoff absorption (top) and bottom depth (bottom) for the simultaneous determination of two fit parameters. Fit parameters are a Y ( 440 nm ) and C P for the left panel, and z B and C P for the right. If not fitted, C X = 2.0 mg ∕l , a Y ( 440 nm ) = 0.3 m - 1 , and z B = 3 m . The bottom type is sediment.

Fig. 8
Fig. 8

Relative error of the phytoplankton concentration for the simultaneous determination of three fit parameters C P , C X , and z B . The correct values of a Y ( 440 nm ) = 0.3 m - 1 and the bottom albedo of sediment were fixed during the inversion.

Fig. 9
Fig. 9

Frequency distribution of the relative errors of (a) C P , (b) C X , (c) ( 440 nm ) , and (d) z B by inversion of the Hydrolight spectra of the remote sensing reflectance and by fitting all four parameters simultaneously. The bottom type was macrophyte.

Fig. 10
Fig. 10

Relative error of the retrieved phytoplankton concentration (top) and bottom depth (bottom) at the fitting spectra of R r s depending on signal noise δ, radiometric resolution Δ R r s , and spectral resolution Δλ . Not fitted parameters were fixed during the inversion at their correct values C P = 2 µg l , C X = 2 mg ∕l , a Y ( 440 nm ) = 0.3 m - 1 , and z B = 3 m . The bottom type was sediment.

Tables (4)

Tables Icon

Table 1 Empirical Coefficients of the Analytical Model of the Irradiance and Remote Sensing Reflectance in Shallow Water

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Table 2 Water Constituent Concentrations and Bottom Depths Used for Hydrolight Simulations

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Table 3 Mean Values of the Relative Error and Standard Deviations a

Tables Icon

Table 4 Mean Relative Errors a

Equations (15)

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R = R { 1 - A 1 exp [ - ( K d + K u , W ) z B ] } + A 2 R B exp { - ( K d + K u , B ) z B ] ,
R r s = R r s , { 1 - A r s , 1 exp [ - ( K d + k u , W ) z B ] } + A r s , 2 R B π exp [ - ( K d + k u , B ) z B ] ,
K d = κ 0 a + b b cos θ s ,
K u , W = ( a + b b ) ( 1 + ω b ) κ 1 , W ( 1 + κ 2 , W cos θ s ) ,
K u , B = ( a + b b ) ( 1 + ω b ) κ 1 , B ( 1 + κ 2 , B cos θ s ) .
f ° = p 1 ( 1 + p 2 ω b + p 3 ω b 2 + p 4 ω b 3 ) ( 1 + p 5 1 cos θ s ) ( 1 + p 6 u ) ,
f = p r s , 1 ( 1 + p r s , 2 ω b + p r s , 3 ω b 2 + p r s , 4 ω b 3 ) × ( 1 + p r s , 5 1 cos θ s ) ( 1 + p r s , 6 u ) ( 1 + p r s , 7 1 cos θ v ) ,
Δ = 1 N λ i = 1 N λ g i X 0 , i - X i 2 ,
z B = 1 2 K d ln ( A 1 R - A 2 R B R - R ) ,
z B = 1 K d ( 1 + 1 cos θ v ) ln ( A r s , 1 R r s , - A r s , 2 R B π R r s , - R r s ) .
C X = ( a W + ½ b W ) - ½ b W b b , X * ( 1 - ) ,
C X = R ( a W + ½ b W ) - ½ b W b b , X * ( 1 - R ) ,
R - A 2 R B exp ( - 2 K d z B ) f ° [ 1 - A 1 exp ( - 2 K d z B ) ] ,
R R r s - A r s , 2 R B π exp [ - K d ( 1 + 1 / cos θ v ) z B ] f { 1 - A r s , 1 exp [ - K d ( 1 + 1 / cos θ v ) z B ] } .
A i + 1 = { A i + Δ i , if   δ < 0 A i - Δ i , if   δ > 0 .

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