Abstract

Ocean physical-biological-optical ecosystem models can require light calculations at thousands of grid points and time steps. Implicit inverse models that recover ocean absorption and scattering properties from measured light variables can require thousands of solutions of the radiative transfer equation. An extremely fast radiative transfer code, EcoLight-S(ubroutine), has been developed to address these needs. EcoLight-S requires less than one second on a moderately fast computer to compute spectral irradiances over near-ultraviolet to near-infrared wavelengths with errors in the photosyntheically available radiation (PAR) of no more than ten percent throughout the euphotic zone. It is thus possible to replace simple and often inaccurate analytical PAR or spectral irradiance models with more accurate radiative transfer calculations, with very little computational penalty. EcoLight-S is applicable to Case 2 and optically shallow waters for which no analytical light models exist. EcoLight-S also computes upwelling and downwelling plane irradiances, nadir and zenith radiances, and the remote-sensing reflectance. These quantities allow ecosystem predictions to be validated with optical measurements obtained from in-water instruments or remotely sensed imagery.

© 2011 OSA

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References

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  1. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994), http://www.curtismobley.com/lightandwater.zip .
  2. C. D. Mobley and L. K. Sundman, HydroLight User’s Guide (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .
  3. C. D. Mobley and L. K. Sundman, HydroLight Technical Documentation (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .
  4. C. D. Mobley, EcoLight-S 1.0 User’s Guide and Technical Documentation (Sequoia Scientific, Inc., 2011), http://www.hydrolight.info .
    [PubMed]
  5. G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. Jaffe, ed., Proc. SPIE2258 (with corrections), 194–201 (1994).
    [CrossRef]
  6. C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
    [CrossRef]
  7. W. Freda and J. Piskozub, “Improved method of Fournier-Forand marine phase function parameterization,” Opt. Express 15(20), 12763–21768 (2007).
    [CrossRef] [PubMed]
  8. W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
    [CrossRef]
  9. W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
    [CrossRef]
  10. C. D. Mobley, “A new IOP model for Case 1 water,” in Ocean Optics Web Book, http://www.oceanopticsbook.info/view/optical_constituents_of_the_ocean/__level_2/a_new_iop_model_for_case_1_water .
  11. C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
    [CrossRef]
  12. A. F. Shchepetkin and J. C. McWilliams, “The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model,” Ocean Model. 9, 347–404 (2005), https://www.myroms.org/wiki/index.php/Documentation_Portal .
    [CrossRef]
  13. F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).
  14. M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
    [CrossRef]
  15. F. Chai, “Incorporating optics into physical and ecosystem modeling,” presented at the Gordon Research Conference on Coastal Ocean Modeling, South Hadley, MA, 26 June–1 July, 2011.
  16. E. Rehm, C. D. Mobley, and J. Smart, “Inverting light with constraints,” presented at Ocean Optics XIX, Barga, Italy, 6–10 Oct. 2008, http://staff.washington.edu/erehm/OOXIX-Rehm-final.pdf .

2009

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

2007

M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
[CrossRef]

W. Freda and J. Piskozub, “Improved method of Fournier-Forand marine phase function parameterization,” Opt. Express 15(20), 12763–21768 (2007).
[CrossRef] [PubMed]

2005

A. F. Shchepetkin and J. C. McWilliams, “The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model,” Ocean Model. 9, 347–404 (2005), https://www.myroms.org/wiki/index.php/Documentation_Portal .
[CrossRef]

2002

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
[CrossRef]

Barber, R. T.

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

Bissett, W. P.

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
[CrossRef]

W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
[CrossRef]

Boss, E.

M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
[CrossRef]

C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
[CrossRef]

Cahill, B.

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

Carder, K. L.

W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
[CrossRef]

W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
[CrossRef]

Chai, F.

M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
[CrossRef]

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

F. Chai, “Incorporating optics into physical and ecosystem modeling,” presented at the Gordon Research Conference on Coastal Ocean Modeling, South Hadley, MA, 26 June–1 July, 2011.

Dieterle, D. A.

W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
[CrossRef]

W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
[CrossRef]

Dugdale, R. C.

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

Forand, J. L.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. Jaffe, ed., Proc. SPIE2258 (with corrections), 194–201 (1994).
[CrossRef]

Fournier, G. R.

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. Jaffe, ed., Proc. SPIE2258 (with corrections), 194–201 (1994).
[CrossRef]

Freda, W.

Fujii, M.

M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
[CrossRef]

McWilliams, J. C.

A. F. Shchepetkin and J. C. McWilliams, “The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model,” Ocean Model. 9, 347–404 (2005), https://www.myroms.org/wiki/index.php/Documentation_Portal .
[CrossRef]

Mobley, C. D.

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
[CrossRef]

E. Rehm, C. D. Mobley, and J. Smart, “Inverting light with constraints,” presented at Ocean Optics XIX, Barga, Italy, 6–10 Oct. 2008, http://staff.washington.edu/erehm/OOXIX-Rehm-final.pdf .

C. D. Mobley and L. K. Sundman, HydroLight User’s Guide (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994), http://www.curtismobley.com/lightandwater.zip .

C. D. Mobley and L. K. Sundman, HydroLight Technical Documentation (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

C. D. Mobley, EcoLight-S 1.0 User’s Guide and Technical Documentation (Sequoia Scientific, Inc., 2011), http://www.hydrolight.info .
[PubMed]

Peng, T.-H.

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

Piskozub, J.

Rehm, E.

E. Rehm, C. D. Mobley, and J. Smart, “Inverting light with constraints,” presented at Ocean Optics XIX, Barga, Italy, 6–10 Oct. 2008, http://staff.washington.edu/erehm/OOXIX-Rehm-final.pdf .

Shchepetkin, A. F.

A. F. Shchepetkin and J. C. McWilliams, “The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model,” Ocean Model. 9, 347–404 (2005), https://www.myroms.org/wiki/index.php/Documentation_Portal .
[CrossRef]

Smart, J.

E. Rehm, C. D. Mobley, and J. Smart, “Inverting light with constraints,” presented at Ocean Optics XIX, Barga, Italy, 6–10 Oct. 2008, http://staff.washington.edu/erehm/OOXIX-Rehm-final.pdf .

Sundaman, L. K.

C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
[CrossRef]

Sundman, L. K.

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

C. D. Mobley and L. K. Sundman, HydroLight User’s Guide (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

C. D. Mobley and L. K. Sundman, HydroLight Technical Documentation (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

Walsh, J. J.

W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
[CrossRef]

W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
[CrossRef]

Wilkerson, F. P.

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

Appl. Opt.

C. D. Mobley, L. K. Sundaman, and E. Boss, “Phase function effects on oceanic light fields,” Appl. Opt. 41(6), 1036–1050 (2002).
[CrossRef]

Biogeosci. Discuss.

C. D. Mobley, L. K. Sundman, W. P. Bissett, and B. Cahill, “Fast and accurate irradiance calculations for ecosystem models,” Biogeosci. Discuss. 6, 10625–10662 (2009), http://www.biogeosciences-discuss.net/6/10625/2009/bgd-6-10625-2009.pdf .
[CrossRef]

Biogeosciences

M. Fujii, E. Boss, and F. Chai, “The value of adding optics to ecosystem models: a case study,” Biogeosciences 4, 817–835 (2007), http://www.biogeosciences.net/4/817/2007/ .
[CrossRef]

Deep-Sea Res.

W. P. Bissett, J. J. Walsh, D. A. Dieterle, and K. L. Carder, “Carbon cycling in the upper waters of the Sargasso Sea: I. numerical simulation of differential carbon and nitrogen fluxes,” Deep-Sea Res. 46, 205–269 (1999a).
[CrossRef]

W. P. Bissett, K. L. Carder, J. J. Walsh, and D. A. Dieterle, “Carbon cycling in the upper waters of the Sargasso Sea: II. numerical simulation of apparent and inherent optical properties,” Deep-Sea Res. 46, 271–317 (1999b).
[CrossRef]

F. Chai, R. C. Dugdale, T.-H. Peng, F. P. Wilkerson, and R. T. Barber, “One dimensional ecosystem model of the equatorial Pacific upwelling system, part I: model development and silicon and nitrogen cycle,” Deep-Sea Res., Part II  49, (13–14), 2713–2745 (2002).

Ocean Model.

A. F. Shchepetkin and J. C. McWilliams, “The regional ocean modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model,” Ocean Model. 9, 347–404 (2005), https://www.myroms.org/wiki/index.php/Documentation_Portal .
[CrossRef]

Opt. Express

Other

C. D. Mobley, “A new IOP model for Case 1 water,” in Ocean Optics Web Book, http://www.oceanopticsbook.info/view/optical_constituents_of_the_ocean/__level_2/a_new_iop_model_for_case_1_water .

F. Chai, “Incorporating optics into physical and ecosystem modeling,” presented at the Gordon Research Conference on Coastal Ocean Modeling, South Hadley, MA, 26 June–1 July, 2011.

E. Rehm, C. D. Mobley, and J. Smart, “Inverting light with constraints,” presented at Ocean Optics XIX, Barga, Italy, 6–10 Oct. 2008, http://staff.washington.edu/erehm/OOXIX-Rehm-final.pdf .

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994), http://www.curtismobley.com/lightandwater.zip .

C. D. Mobley and L. K. Sundman, HydroLight User’s Guide (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

C. D. Mobley and L. K. Sundman, HydroLight Technical Documentation (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

C. D. Mobley, EcoLight-S 1.0 User’s Guide and Technical Documentation (Sequoia Scientific, Inc., 2011), http://www.hydrolight.info .
[PubMed]

G. R. Fournier and J. L. Forand, “Analytic phase function for ocean water,” in Ocean Optics XII, J. Jaffe, ed., Proc. SPIE2258 (with corrections), 194–201 (1994).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Example simulation showing the use of dynamic solution depths for RTE solutions down to the depth where the scalar irradiance has decreased to 10% of the surface value.

Fig. 2
Fig. 2

Errors in PAR for different dynamic solution depths for the same environmental conditions as Fig. 1. The color-coded inset in the second panel shows the value of F o, the wavelength resolution (always 5 nm for this figure, corresponding to nwskip = 0), and the run time in seconds. The dots along the PAR profiles show the greatest RTE solution depth (after the solution for the first wavelength) for each of the simulations, e.g., 32.5 m for the simulation of Fig. 1, which is the purple curve in this figure. The third panel shows the relative errors in PAR compared to the unoptimized run, and the rightmost panel shows the actual PAR errors.

Fig. 3
Fig. 3

Errors in PAR for different wavelength resolutions (different values of nwskip) compared to 5 nm bands from 400 to 700 nm, for the same environmental conditions as Fig. 1.

Fig. 4
Fig. 4

Errors in PAR for combinations of solution depths (F o values) and wavelength skipping (nwskip values; the labels show the resulting wavelength resolution) compared to solutions to 50 m for 5 nm bands from 400 to 700 nm. The environmental conditions are the same as for Fig. 1.

Fig. 5
Fig. 5

Scalar irradiances for unoptimized (E o(un), upper left panel) and optimized (E o(op), upper right panel) solutions. The optimized solution corresponds to the orange curve of Fig. 4. The lower left panel shows the relative errors E o computed as in Eq. (11), and the lower right panel shows the actual errors in E o.

Fig. 6
Fig. 6

Errors in PAR for the same simulations as Fig. 4, but with a one-meter depth resolution.

Fig. 7
Fig. 7

Differences in PAR for different depth resolutions of the continuous chlorophyll profile of Fig. 1, for unoptimized solutions.

Fig. 8
Fig. 8

Remote-sensing reflectances R rs for the pure water and Case 2 runs of Table 2. The solid curves are the HydroLight 5.1 runs with inelastic scattering. The open circles are the unoptimized EcoLight-S runs, and the filled dots are EcoLight-S with F o = 0.2.

Tables (2)

Tables Icon

Table 1 Effect of Layer Thickness on PAR Values at 15 m for the Environmental Conditions of Fig. 1 *

Tables Icon

Table 2 Simulations of Pure Water and Turbid Case 2 Water

Equations (13)

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

cos θ d L ( z , θ , ϕ , λ ) d z = c ( z , λ ) L ( z , θ , ϕ , λ ) + 0 2 π 0 π β ( z , θ , ϕ , θ , ϕ , λ ) L ( z , θ , ϕ , λ ) sin θ d θ d ϕ + S ( z , θ , ϕ , λ ) .
E o ( z , λ ) = 0 2 π 0 π L ( z , θ , ϕ , λ ) sin θ d θ d ϕ
P A R ( z ) = 400 700 λ h c E o ( z , λ ) d λ .
T ( z , t ) t = 1 ρ c p [ E ¯ d ( z , t ) E ¯ u ( z , t ) ] z ,
E ¯ d ( z ) = 400 1000 0 2 π 0 π / 2 L ( z , θ , ϕ , λ ) cos θ sin θ d θ d ϕ d λ ,
cos θ d L ( z , θ , λ ) d z = c ( z , λ ) L ( z , θ , λ ) + 0 π β ( z , θ , θ , λ ) L ( z , θ , λ ) sin θ d θ ,
β ( z , θ , θ , λ ) = 0 2 π β ( z , θ , ϕ , θ , ϕ = 0 , λ ) d ϕ
L ( z , θ , λ ) = 0 2 π L ( z , θ , ϕ , λ ) d ϕ ,
E o ( z o , λ ) = E o ( 0 , λ ) exp [ 0 z o K o ( z , λ ) d z ] .
F o = E o ( z o , λ ) E o ( 0 , λ ) exp [ 0 z o a ( z , λ ) d z ] .
μ ¯ d ( z k ) = E d ( z k ) E od ( z k )     and     μ ¯ ( z k ) = E d ( z k ) E u ( z k ) E o ( z k )
E o ( z , λ ) = E o ( z k , λ ) exp [ z k z a ( z , λ ) μ ¯ ( z k , λ ) d z ] .
relative error = 100 P A R ( optimized ) P A R ( unoptimized ) P A R ( unoptimized ) ,

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