Abstract

The vertical spectral diffuse attenuation coefficient of Kd is an important optical property related to the penetration and availability of light underwater, which is of fundamental interest in studies of ocean physics and biology. Models developed in the recent decades were mainly based on theoretical analyses and numerical (radiative transfer) simulations to estimate this property in optically deep waters, thus leaving inadequate knowledge of its variability at multiple depths and wavelengths, covering a wide range of solar incident geometry, in turbid coastal waters. In the present study, a new model is developed to quantify the vertical, spatial and temporal variability of Kd at multiple wavelengths and to quantify its dependence with respect to solar incident geometry under differing sky conditions. Thus, the new model is derived as a function of inherent optical properties (IOPs – absorption a and backscattering bb), solar zenith angle and depth parameters. The model results are rigorously evaluated using time-series and discrete in situ data from clear and turbid coastal waters. The Kd values derived from the new model are found to agree with measured data within the mean relative error 0.02~6.24% and R2 0.94~0.99. By contrast, the existing models have large errors when applied to the same data sets. Statistical results of the new model for the vertical spectral distribution of Kd in clear oceanic waters (for different solar zenith and in-water conditions) are also good when compared to those of the existing models. These results suggest that the new model can provide an improved interpretation about the variation of the vertical spectral diffuse attenuation coefficient of downwelling irradiance, which will have important implications for ocean physics, biogeochemical cycles and underwater applications in both relatively clear and turbid coastal waters.

© 2013 Optical Society of America

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2013 (2)

Z. Lee, C. Hu, S. Shang, K. Du, M. Lewis, R. Arnone, and R. Brewin, “Penetration of UV-visible solar radiation in the global oceans: Insights from ocean color remote sensing,” J. Geophys. Res.118, 1–15 (2013), doi:.
[CrossRef]

V. B. Sundarabalan, P. Shanmugam, and S. S. Manjusha, “Radiative transfer modeling of upwelling light field in coastal waters,” J. Quant. Spectrosc. Radiat. Transfer121, 30–44 (2013).
[CrossRef]

2012 (1)

K. Gao, E. W. Helbling, D. P. Hader, and D. A. Hutchins, “Responses of marine primary producers to interactions between ocean acidification, solar radiation, and warming,” Mar. Ecol. Prog. Ser.470, 167–189 (2012).
[CrossRef]

2011 (1)

P. Shanmugam, V. B. Sundarabalan, Y. H. Ahn, and J. H. Ryu, “A new inversion model to retrieve the particulate backscattering in coastal/ocean waters,” IEEE Trans. Geosci. Remote Sens.49(6), 2463–2475 (2011).
[CrossRef]

2010 (1)

X. Pan and R. C. Zimmerman, “Modeling the vertical distributions of downwelling plane irradiance and diffuse attenuation coefficient in optically deep waters,” J. Geophys. Res.115, C08016 (2010), doi:.
[CrossRef]

2009 (1)

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009), doi:.
[CrossRef]

2007 (3)

Y.-H. Ahn and P. Shanmugam, “Derivation and analysis of the fluorescence algorithms to estimate phytoplankton pigment concentrations in optically complex coastal waters,” J. Opt. A Pure Appl. Opt.9, 352–362 (2007).
[CrossRef]

D. P. Häder, H. D. Kumar, R. C. Smith, and R. C. Worrest, “Effects of solar UV radiation on aquatic ecosystems and interactions with climate change,” Photochem. Photobiol. Sci.6(3), 267–285 (2007).
[CrossRef] [PubMed]

A. Morel, Y. Huot, B. Gentili, P. J. Werdell, S. B. Hooker, and B. A. Franz, “Examining the consistency of products derived from various ocean color sensors in open ocean (Case 1) waters in the perspective of a multi-sensor approach,” Remote Sens. Environ.111(1), 69–88 (2007), doi:.
[CrossRef]

2005 (1)

Z. P. Lee, K. P. Du, and R. Arnone, “A model for diffuse attenuation coefficient of downwelling irradiance,” J. Geophys. Res.110, C02016 (2005), doi:.
[CrossRef]

2004 (2)

G. C. Chang and T. D. Dickey, “Coastal ocean optical influences on solar transmission and radiant heating rate,” J. Geophys. Res.109, C01020 (2004), doi:.
[CrossRef]

C. R. McClain, G. C. Feldman, and S. B. Hooker, “An overview of the SeaWiFS project and strategies for producing a climate research quality global ocean bio-optical time series,” Deep Sea Res. Part II Top. Stud. Oceanogr.51(1–3), 5–42 (2004), doi:.
[CrossRef]

2003 (2)

J. T. O. Kirk, “The vertical attenuation of irradiance as a function of the optical properties of the water,” Limnol. Oceanogr.48(1), 9–17 (2003).
[CrossRef]

T. Ohde and H. Siegel, “Derivation of immersion factors for the hyperspectral TriOS radiance sensor,” J. Opt. A, Pure Appl. Opt.5(3), L12–L14 (2003).
[CrossRef]

2002 (4)

1998 (4)

A. Morel and H. Loisel, “Apparent optical properties of oceanic water: Dependence on the molecular scattering contribution,” Appl. Opt.37(21), 4765–4776 (1998).
[CrossRef] [PubMed]

Z. P. Lee, K. L. Carder, C. D. Mobley, R. G. Steward, and J. S. Patch, “Hyperspectral remote sensing for shallow waters. I. A semianalytical model,” Appl. Opt.37(27), 6329–6338 (1998).
[CrossRef] [PubMed]

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr.43(4), 564–576 (1998).
[CrossRef]

W. E. Esaias, M. R. Abbott, I. Barton, O. B. Brown, J. W. Campbell, K. L. Carder, D. K. Clark, R. H. Evans, F. E. Hoge, H. R. Gordon, W. M. Balch, R. Letelier, and P. J. Minnett, “An overview of MODIS capabilities for ocean science observations,” IEEE Trans. Geosci. Rem. Sens.36(4), 1250–1265 (1998), doi:.
[CrossRef]

1997 (2)

M. A. Moran and R. G. Zepp, “Role of photoreactions in the formation of biologically labile compounds from dissolved organic matter,” Limnol. Oceanogr.42(6), 1307–1316 (1997).
[CrossRef]

W. S. Pegau, D. Gray, and J. R. V. Zaneveld, “Absorption and attenuation of visible and near-infrared light in water: Dependence on temperature and salinity,” Appl. Opt.36(24), 6035–6046 (1997).
[CrossRef] [PubMed]

1996 (2)

J. C. Ohlmann, D. A. Siegel, and C. Gautier, “Ocean mixed layer radiant heating and solar penetration: A global analysis,” J. Clim.9(10), 2265–2280 (1996).
[CrossRef]

C. R. McClain, K. Arrigo, K. S. Tai, and D. Turk, “Observations and simulations of physical and biological processes at ocean weather station P, 1951–1980,” J. Geophys. Res.101(C2), 3697–3713 (1996).
[CrossRef]

1995 (3)

J. Marra, C. Langdon, and C. A. Knudson, “Primary production, water column changes, and the demise of a phaeocystis bloom at the marine light-mixed layers site (59°N, 21°W) in the northeast Atlantic Ocean,” J. Geophys. Res.100(C4), 6633–6644 (1995).
[CrossRef]

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnol. Oceanogr.40(8), 1347–1357 (1995).
[CrossRef]

N. J. McCormick, “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr.40(5), 1013–1018 (1995).
[CrossRef]

1994 (2)

A. Morel and D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr.24(7), 1652–1665 (1994).
[CrossRef]

J. R. V. Zaneveld, J. C. Kitchen, and C. Moore, “The scattering error correction of reflecting-tube absorption meters,” Proc. SPIE2258, 44–55 (1994).
[CrossRef]

1993 (3)

1992 (1)

T. T. Bannister, “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr.37(4), 773–780 (1992).
[CrossRef]

1991 (1)

J. T. O. Kirk, “Volume scattering function, average cosines, and the underwater light field,” Limnol. Oceanogr.36(3), 455–467 (1991), doi:.
[CrossRef]

1990 (3)

M. R. Lewis, M.-E. Carr, G. C. Feldman, W. Esaias, and C. McMclain, “Influence of penetrating solar radiation on the heat budget of the equatorial Pacific Ocean,” Nature347(6293), 543–545 (1990).
[CrossRef]

C. L. Gallegos, D. L. Correll, R. H. Stavn, and A. D. Weidemann, “Modeling spectral diffuse attenuation, absorption, and scattering coefficients in a turbid estuary,” Limnol. Oceanogr.35(7), 1486–1502 (1990).
[CrossRef]

M. R. Lewis, M.-E. Carr, G. C. Feldman, W. Esaias, and C. McClain, “Influence of penetrating solar radiation on the heat budget of the equatorial Pacific Ocean,” Nature347(6293), 543–545 (1990).
[CrossRef]

1989 (4)

S. Sathyendranath, T. Platt, C. M. Caverhill, R. E. Warnock, and M. R. Lewis, “Remote sensing of oceanic primary production: Computations using a spectral model,” Deep Sea Res. Part II Top. Stud. Oceanogr.36, 431–453 (1989).

R. H. Stavn and A. D. Weidemann, “Shape factors, two-flow models, and the problem of irradiance inversion in estimating optical parameters,” Limnol. Oceanogr.34(8), 1426–1441 (1989).
[CrossRef]

H. R. Gordon, “Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water?” Limnol. Oceanogr.34(8), 1389–1409 (1989).
[CrossRef]

J. R. V. Zaneveld, “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr.34(8), 1442–1452 (1989), doi:.
[CrossRef]

1988 (3)

S. Sathyendranath and T. Platt, “The spectral irradiance field at the surface and in the interior of the ocean: A model for applications in oceanography and remote sensing,” J. Geophys. Res.93(C8), 9270–9280 (1988).
[CrossRef]

A. Morel, “Optical modeling of the upper ocean in relation to its biogenous matter content (case 1 waters),” J. Geophys. Res.93(C9), 10,749–10,768 (1988), doi:.
[CrossRef]

T. Platt, S. Sathyendranath, C. M. Caverhill, and M. Lewis, “Ocean primary production and available light: Further algorithms for remote sensing,” Deep Sea Res.35(6), 855–879 (1988).
[CrossRef]

1984 (1)

J. T. O. Kirk, “Dependence of relationship between inherent and apparent optical properties of water on solar altitude,” Limnol. Oceanogr.29(2), 350–356 (1984).
[CrossRef]

1981 (2)

J. J. Simpson and T. D. Dickey, “The relationship between downward irradiance and upper Ocean structure,” J. Phys. Oceanogr.11(3), 309–323 (1981).
[CrossRef]

R. C. Smith and K. S. Baker, “Optical properties of the clearest natural waters (200-800 nm),” Appl. Opt.20(2), 177–184 (1981).
[CrossRef] [PubMed]

1980 (1)

K. S. Baker and R. C. Smith, “Quasi-inherent characteristics of the diffuse attenuation coefficient for irradiance,” Proc. SPIE208, 60–63 (1980).
[CrossRef]

1975 (1)

Abbott, M. R.

W. E. Esaias, M. R. Abbott, I. Barton, O. B. Brown, J. W. Campbell, K. L. Carder, D. K. Clark, R. H. Evans, F. E. Hoge, H. R. Gordon, W. M. Balch, R. Letelier, and P. J. Minnett, “An overview of MODIS capabilities for ocean science observations,” IEEE Trans. Geosci. Rem. Sens.36(4), 1250–1265 (1998), doi:.
[CrossRef]

Ahn, Y. H.

P. Shanmugam, V. B. Sundarabalan, Y. H. Ahn, and J. H. Ryu, “A new inversion model to retrieve the particulate backscattering in coastal/ocean waters,” IEEE Trans. Geosci. Remote Sens.49(6), 2463–2475 (2011).
[CrossRef]

Ahn, Y.-H.

Y.-H. Ahn and P. Shanmugam, “Derivation and analysis of the fluorescence algorithms to estimate phytoplankton pigment concentrations in optically complex coastal waters,” J. Opt. A Pure Appl. Opt.9, 352–362 (2007).
[CrossRef]

Antoine, D.

A. Morel and D. Antoine, “Heating rate within the upper ocean in relation to its bio-optical state,” J. Phys. Oceanogr.24(7), 1652–1665 (1994).
[CrossRef]

Arnone, R.

Z. Lee, C. Hu, S. Shang, K. Du, M. Lewis, R. Arnone, and R. Brewin, “Penetration of UV-visible solar radiation in the global oceans: Insights from ocean color remote sensing,” J. Geophys. Res.118, 1–15 (2013), doi:.
[CrossRef]

Z. P. Lee, K. P. Du, and R. Arnone, “A model for diffuse attenuation coefficient of downwelling irradiance,” J. Geophys. Res.110, C02016 (2005), doi:.
[CrossRef]

Arnone, R. A.

Arrigo, K.

C. R. McClain, K. Arrigo, K. S. Tai, and D. Turk, “Observations and simulations of physical and biological processes at ocean weather station P, 1951–1980,” J. Geophys. Res.101(C2), 3697–3713 (1996).
[CrossRef]

Baker, K. S.

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M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009), doi:.
[CrossRef]

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J. C. Ohlmann, D. A. Siegel, and C. Gautier, “Ocean mixed layer radiant heating and solar penetration: A global analysis,” J. Clim.9(10), 2265–2280 (1996).
[CrossRef]

Siegel, H.

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[CrossRef]

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J. J. Simpson and T. D. Dickey, “The relationship between downward irradiance and upper Ocean structure,” J. Phys. Oceanogr.11(3), 309–323 (1981).
[CrossRef]

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D. P. Häder, H. D. Kumar, R. C. Smith, and R. C. Worrest, “Effects of solar UV radiation on aquatic ecosystems and interactions with climate change,” Photochem. Photobiol. Sci.6(3), 267–285 (2007).
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M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009), doi:.
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[CrossRef]

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[CrossRef]

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Stramski, D.

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr.43(4), 564–576 (1998).
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Figures (14)

Fig. 1
Fig. 1

(a) Location map with sampling stations in coastal waters off Point Calimere on the southeast part of India. In situ measurements were made before and during the southwest monsoon (13–21 May 2012 and 15-18 August 2012 respectively). (b) The nature of waters sampled off Chennai and Point Calimere (c-e). (d-e) Characteristic features of coastal waters at a time series station off Point Calimere.

Fig. 2
Fig. 2

Dependency of the newly defined parameters A1, A2, C1, C2 on θ, bb/a and depth.

Fig. 3
Fig. 3

The depth-averaged vertical profiles of the absorption coefficients (a), backscattering coefficients (bb) at different wavelengths (412, 443, 490, 510 and 551 nm) measured (time series) during the May 2012 (before southwest monsoon) and August 2012 (during southwest monsoon) cruises in coastal waters off Point Calimere of southern India. Note that the negative sign indicates before noon and the positive sign indicates after noon for describing the solar zenith angle.

Fig. 4
Fig. 4

The depth-averaged vertical profiles of the absorption coefficients (a), backscattering coefficients (bb) at different wavelengths measured during the May 2012 (before the southwest monsoon) and August 2012 (during the southwest monsoon) cruises in coastal waters off Point Calimere of southern India.

Fig. 5
Fig. 5

The depth-averaged vertical profiles of the absorption coefficients (a) and backscattering coefficients (bb) measured in clear waters of Chennai during August 2013.

Fig. 6
Fig. 6

Comparison of the diffuse attenuation coefficient Kd(λ) derived from the new model and existing models for different depth layers (z) at the time series coastal station (relatively clear to turbid waters) off Point Calimere before and during the southwest monsoon (May 2012 and August 2012 respectively). (a) Diffuse attenuation coefficient just below the surface, (b) Diffuse attenuation coefficient at the intermediate layer, (c) Diffuse attenuation coefficient at the bottom layer.

Fig. 7
Fig. 7

Comparison of the diffuse attenuation coefficient Kd(λ) derived from the new model and existing models for different depth layers (z) at different coastal stations (relatively clear to turbid waters) off Point Calimere before and during the southwest monsoon (May 2012 and August 2012 respectively). (a) Diffuse attenuation coefficient just below the surface, (b) Diffuse attenuation coefficient at the intermediate layer, (c) Diffuse attenuation coefficient at the bottom layer.

Fig. 8
Fig. 8

Comparison of the diffuse attenuation coefficient Kd(λ) derived from the new model and existing models for different depth layers (z) at the time series station off Chennai (Clear waters) during the southwest monsoon (31 August 2013). (a) Diffuse attenuation coefficient just below the surface, (b) Diffuse attenuation coefficient at the intermediate layer, (c) Diffuse attenuation coefficient at the bottom layer.

Fig. 9
Fig. 9

Comparison of the modeled Kd(λ) with in situ Kd(λ) for different zenith angles at the time series coastal station off Point Calimere before and during the southwest monsoon: Key wavelengths a) 412nm, b) 443nm, c) 490nm, d) 510nm, e) 531nm, f) 551nm, and g) 670nm. (0, 2 and 3m correspond to different depth layers (z)).

Fig. 10
Fig. 10

Comparison of the modeled Kd(λ) with in situ Kd(λ) for different depth layers (z) at the time series coastal station off Point Calimere before and during the southwest monsoon (May 2012 and August 2012). (a-d) Time series measurements at −43°, −23°, 12°, 51° in May 2012, and −45°, −23°, 3°, 42° in August 2012. Legend: Black line – In situ; Blue line – New model; Red line – Model 1 [15]; Green line – Model 2 [18].

Fig. 11
Fig. 11

Comparison of the modeled Kd(λ) with in situ Kd(λ) for different depth layers (z) at the discrete coastal stations (a-d correspond to St-1, St-2, St-3 and St-4) off Point Calimere before and during the southwest monsoon (May 2012 and August 2012). Black line – In situ; Blue line – New model; Red line – Model 1 [15]; Green line – Model 2 [18].

Fig. 12
Fig. 12

Comparison of the modeled Kd(λ) values from the new model and existing models with in situ Kd(λ) values at some key wavelengths (412, 443, 490, 510, 531,551 and 670 nm) (N = 58) (Top panels – Before the southwest monsoon; Bottom panels – During the southwest monsoon).

Fig. 13
Fig. 13

Statistical comparisons between the modeled and measured Kd values in clear and turbid coastal waters off Point Calimere and Chennai before and during the southwest monsoon (all three cruises data used for this analysis). RMSE – root means square error and MRE – mean relative error. Legend: Blue – New model; Red – Model 1 [15]; Green – Model 2 [18].

Fig. 14
Fig. 14

Relationship between in situ Kd(360) and Kd(490) values from the profile measurements obtained in relatively clear and turbid coastal waters off Point Calimere and Chennai during before and during the southwest monsoon.

Tables (2)

Tables Icon

Table 1 Details of stations sampled before and during the southwest monsoon (13–23 May 2012 and 15–19 August 2012 respectively). Actual depth ≈measurements depth + 2m.

Tables Icon

Table 2 The range of absorption (a), backscattering (bb), Chl and Turbidity at various stations off Point Calimere and Chennai before and during the southwest monsoon.

Equations (23)

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

K d =[ 1 E d d E d dz ].
K d =[ a+ b b cos( θ sw ) ].
K d =1.0395 a+ b b μ w .
K d = ( α 2 +Gab) 1/2 μ w .
K d = a+ b b μ d R b b μ u .
K d = m 0 a+v b b .
K d a+ b b μ d .
K ¯ ( z 1 z 2 ) d = 1 z 2 z 1 ln( E d ( z 1 ) E d ( z 2 ) ).
K ¯ (0 z ' ) d = 0 z ' K d (z)dz z ' .
K d (z)=a+ b b .
K d = (a+ b b ) μ 0 .
K d ( z z 1 ) = 1 ( Z 1 Z ) [ ln E d ( z ) ln E d ( Z 1 ) ] .
K d = [ A ( A 1 a + A 2 b b ) ] + C 3 .
A = 1 C C 1 2 .
C 1 = 4.848 + 0.01696 z 4.84 cos ( θ ) .
C 2 = 14.98 + 0.3228 z 32.32 cos ( θ ) 0.3562 z cos ( θ ) + 17.65 ( cos ( θ ) ) 2 .
C 3 = 13.13 + 0.6286 z + 30.62 cos ( θ ) 0.1292 z 2 0.2724 z cos ( θ ) 17.14 ( cos ( θ ) ) 2 .
A 1 = 1 + cos ( θ ) .
A 2 = [ a 3 + ( b b a ) 2 b b 2 a ( b b a ) 4 ] .
K d = [ ( 1 C 1 C 2 ) ] [ ( 1 + cos ( θ ) ) a + ( a 3 + ( b b a ) 2 b b 2 a ( b b a ) 4 ) b b ] + C 3 .
RMSE= [ i=1 N ( log k d model log k d insitu ) 2 N2 ] 1/2 .
MRE=[ i=1 N log k d model log k d insitu log k d insitu ]×100.
K d ( 360 ) = 0.0386 + 1.6034 K d ( 490 ) ; R 2 = 0. 77 .

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