Abstract

Water-leaving radiance is subject to depth variability of the water constituents. The optical penetration depth is strongly dependent on the wavelength λ, which allows to retrieve a non-uniform vertical profile of an optically-active constituent CTSM(z) from remote-sensing reflectance Rrs(λ,Cz). We define the apparent particle concentration CTSM,app(λ) of a vertically homogeneous water column whose Rrs(λ,Cconst) matches Rrs(λ,Cz). Subsequently, we define a vertically-weighted averaged particle concentration CTSM,ave(λ), only dependent on CTSM(z), and retrieve CTSM(z) by minimizing the error between CTSM,app(λ) and CTSM,ave(λ) with genetic algorithms. We conclude that the retrieval is excellent if the sub-surface maximum lays close to the surface or the background concentration of CTSM(z) is low. Conversely, results worsen for opposite conditions, due to insufficient signal strength from superimposed sub-surface maxima.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2013 (1)

2012 (3)

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

2011 (1)

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

2010 (1)

A. B. Ryabov, L. Rudolf, and B. Blasius, “Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer,” J. Theor. Biol. 263(1), 120–133 (2010).
[CrossRef] [PubMed]

2008 (1)

T. Kutser, L. Metsamaa, and A. G. Dekker, “Influence of the vertical distribution of cyanobacteria in the water column on the remote sensing signal,” Estuar. Coast. Shelf Sci. 78(4), 649–654 (2008).
[CrossRef]

2005 (2)

2003 (1)

K. Fennel and E. Boss, “Subsurface maxima of phytoplankton and chlorophyll: Steady-state solutions from a simple model,” Limnol. Oceanogr. 48(4), 1521–1534 (2003).
[CrossRef]

2001 (1)

P. Forget, P. Broche, and J.-J. Naudin, “Reflectance sensitivity to solid suspended sediment stratification in coastal water and inversion: A case study,” Remote Sens. Environ. 77(1), 92–103 (2001).
[CrossRef]

1997 (1)

1992 (1)

1988 (1)

A. W. Harrison and C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

1981 (1)

1980 (2)

H. R. Gordon and D. K. Clark, “Remote sensing optical properties of a stratified ocean: an improved interpretation,” Appl. Opt. 19(20), 3428–3430 (1980).
[CrossRef] [PubMed]

F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24(2), 177–189 (1980).
[CrossRef]

1978 (1)

Baker, K. S.

Barnard, A.

Blasius, B.

A. B. Ryabov, L. Rudolf, and B. Blasius, “Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer,” J. Theor. Biol. 263(1), 120–133 (2010).
[CrossRef] [PubMed]

Boehrer, B.

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

Boss, E.

J. R. Zaneveld, A. Barnard, and E. Boss, “Theoretical derivation of the depth average of remotely sensed optical parameters,” Opt. Express 13(22), 9052–9061 (2005).
[CrossRef] [PubMed]

K. Fennel and E. Boss, “Subsurface maxima of phytoplankton and chlorophyll: Steady-state solutions from a simple model,” Limnol. Oceanogr. 48(4), 1521–1534 (2003).
[CrossRef]

Brando, V. E.

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

Broche, P.

P. Forget, P. Broche, and J.-J. Naudin, “Reflectance sensitivity to solid suspended sediment stratification in coastal water and inversion: A case study,” Remote Sens. Environ. 77(1), 92–103 (2001).
[CrossRef]

Carpenter, J.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

Clark, D. K.

Clegg, M. R.

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

Coombes, C. A.

A. W. Harrison and C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

Czeplak, G.

F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24(2), 177–189 (1980).
[CrossRef]

Dekker, A. G.

T. Kutser, L. Metsamaa, and A. G. Dekker, “Influence of the vertical distribution of cyanobacteria in the water column on the remote sensing signal,” Estuar. Coast. Shelf Sci. 78(4), 649–654 (2008).
[CrossRef]

Fennel, K.

K. Fennel and E. Boss, “Subsurface maxima of phytoplankton and chlorophyll: Steady-state solutions from a simple model,” Limnol. Oceanogr. 48(4), 1521–1534 (2003).
[CrossRef]

Forget, P.

P. Forget, P. Broche, and J.-J. Naudin, “Reflectance sensitivity to solid suspended sediment stratification in coastal water and inversion: A case study,” Remote Sens. Environ. 77(1), 92–103 (2001).
[CrossRef]

Fry, E. S.

Gaedke, U.

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

Gitelson, A.

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

Gordon, H. R.

Harrison, A. W.

A. W. Harrison and C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

He, M.-X.

Kasten, F.

F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24(2), 177–189 (1980).
[CrossRef]

Kawka, M.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

Klausmeier, C. A.

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

Kutser, T.

T. Kutser, L. Metsamaa, and A. G. Dekker, “Influence of the vertical distribution of cyanobacteria in the water column on the remote sensing signal,” Estuar. Coast. Shelf Sci. 78(4), 649–654 (2008).
[CrossRef]

Litchman, E.

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

Mellard, J. P.

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

Metsamaa, L.

T. Kutser, L. Metsamaa, and A. G. Dekker, “Influence of the vertical distribution of cyanobacteria in the water column on the remote sensing signal,” Estuar. Coast. Shelf Sci. 78(4), 649–654 (2008).
[CrossRef]

Naudin, J.-J.

P. Forget, P. Broche, and J.-J. Naudin, “Reflectance sensitivity to solid suspended sediment stratification in coastal water and inversion: A case study,” Remote Sens. Environ. 77(1), 92–103 (2001).
[CrossRef]

Odermatt, D.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

Pitarch, J.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

Pomati, F.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

Pope, R. M.

Rudolf, L.

A. B. Ryabov, L. Rudolf, and B. Blasius, “Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer,” J. Theor. Biol. 263(1), 120–133 (2010).
[CrossRef] [PubMed]

Ryabov, A. B.

A. B. Ryabov, L. Rudolf, and B. Blasius, “Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer,” J. Theor. Biol. 263(1), 120–133 (2010).
[CrossRef] [PubMed]

Schaepman, M.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

Smith, R. C.

Spijkerman, E.

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

Stramska, M.

Stramski, D.

Wüest, A.

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

Yang, Q.

Yoshiyama, K.

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

Zaneveld, J. R.

Appl. Opt. (7)

Estuar. Coast. Shelf Sci. (1)

T. Kutser, L. Metsamaa, and A. G. Dekker, “Influence of the vertical distribution of cyanobacteria in the water column on the remote sensing signal,” Estuar. Coast. Shelf Sci. 78(4), 649–654 (2008).
[CrossRef]

J. Theor. Biol. (2)

A. B. Ryabov, L. Rudolf, and B. Blasius, “Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer,” J. Theor. Biol. 263(1), 120–133 (2010).
[CrossRef] [PubMed]

J. P. Mellard, K. Yoshiyama, E. Litchman, and C. A. Klausmeier, “The vertical distribution of phytoplankton in stratified water columns,” J. Theor. Biol. 269(1), 16–30 (2011).
[CrossRef] [PubMed]

Limnol. Oceanogr. (1)

K. Fennel and E. Boss, “Subsurface maxima of phytoplankton and chlorophyll: Steady-state solutions from a simple model,” Limnol. Oceanogr. 48(4), 1521–1534 (2003).
[CrossRef]

Oecologia (1)

M. R. Clegg, U. Gaedke, B. Boehrer, and E. Spijkerman, “Complementary ecophysiological strategies combine to facilitate survival in the hostile conditions of a deep chlorophyll maximum,” Oecologia 169(3), 609–622 (2012).
[CrossRef] [PubMed]

Opt. Express (1)

Remote Sens. Environ. (3)

D. Odermatt, F. Pomati, J. Pitarch, J. Carpenter, M. Kawka, M. Schaepman, and A. Wüest, “MERIS observations of phytoplankton blooms in a stratified eutrophic lake,” Remote Sens. Environ. 126, 232–239 (2012).
[CrossRef]

P. Forget, P. Broche, and J.-J. Naudin, “Reflectance sensitivity to solid suspended sediment stratification in coastal water and inversion: A case study,” Remote Sens. Environ. 77(1), 92–103 (2001).
[CrossRef]

D. Odermatt, A. Gitelson, V. E. Brando, and M. Schaepman, “Review of constituent retrieval in optically deep and complex waters from satellite imagery,” Remote Sens. Environ. 118, 116–126 (2012).
[CrossRef]

Sol. Energy (2)

A. W. Harrison and C. A. Coombes, “An opaque cloud cover model of sky short wavelength radiance,” Sol. Energy 41(4), 387–392 (1988).
[CrossRef]

F. Kasten and G. Czeplak, “Solar and terrestrial radiation dependent on the amount and type of cloud,” Sol. Energy 24(2), 177–189 (1980).
[CrossRef]

Other (3)

C. D. Mobley and L. K. Sundman, Hydrolight 5 Technical Documentation (Sequoia Scientific, Inc., 2008), http://www.hydrolight.info .

L. Davis, Handbook of genetic algorithms (Van Nostrand Reinhold, New York, 1991).

P. Gege, “Characterization of the phytoplankton in Lake Constance for classification by remote sensing (with 6 figures and 2 tables),” in Lake Constance, Characterization of an Ecosystem in Transition, E. Baeuerle and U. Gaedke, eds. (E. Schweizerbart'sche Verlagsbuchhandlung (Nägele und Obermiller), 1998), pp. 179–194.

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Figures (6)

Fig. 1
Fig. 1

(a): Set of 25 CTSM,const, from 0 to 1.2 mg l−1, in different colors. Superimposed is an arbitrary example profile CTSM(z) in black thick. (b): LUT of Rrs(λ,Cconst) associated to the corresponding 25 CTSM,const values from panel (a). Superimposed in black thick, Rrs(λ,Cz) corresponding to CTSM(z) in panel (a). (c) Apparent CTSM,app(λ), derived from the pair CTSM(z) and Rrs(λ,Cz) as read out from the LUT in panel (b). Reading example: Rrs(450,Cz) = Rrs(450,Cconst) for CTSM,const = 0.7 mg l−1, therefore CTSM,app(450) = 0.7 mg l−1 (Fig. 1(c)).

Fig. 2
Fig. 2

CTSM,app(λ) (blue) and CTSM,ave(λ,psol) (red) calculated for 32 independent TSM profiles randomly chosen from the 3024 simulations of the SDS of Table 2.

Fig. 3
Fig. 3

Construction of the goal function fx(x) to retrieve the shape x of the unknown profile. From Rrs(λ,Cz), CTSM,app(λ) is obtained by LUT search. In parallel, a guess of solution x is used to build a vertical TSM profile, which is vertically averaged by Eq. (11) to obtain CTSM,ave(λ,x). Finally, the goal function is constructed as the wavelength average of the difference between CTSM,ave(λ,x) and CTSM,app(λ).

Fig. 4
Fig. 4

Selected original (blue) and retrieved (red) profiles, with the corresponding distance d (Eq. (18)) for each retrieval. Axes are equal for all plots (bottom left) and are omitted for readability.

Fig. 5
Fig. 5

For every value of the Gaussian parameters Cbg, Cmax, σ and zmax (horizontal axis of each graph) the arithmetic mean of the other three parameters, belonging to the fraction of well-retrieved profiles of the SDS (d < 0.4), are shown (continuous lines). Blue: Cbg. Green: Cmax. Red: σ. Cyan: zmax. In the same colors, the mean values of each parameter for all the SDS are plotted (dashed lines). Note that, in graph (d), all zmax values are grouped in intervals.

Fig. 6
Fig. 6

Fraction of well-retrieved profiles (d < 0.4) discriminated for the values of the Gaussian parameters Cbg, Cmax, σ and zmax. The different colors correspond to different values of the wavelength step δλ.

Tables (2)

Tables Icon

Table 1 Symbols used in this study

Tables Icon

Table 2 Gaussian parameters to build the SDS containing 3024 simulations.

Equations (18)

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

C TSM ( z ) = C bg + C max exp [ 1 2 ( z z max σ ) 2 ]
a( λ,z )= a w ( λ )+ a ph ( λ )+ a g ( λ )+ a NAP ( λ,z ) b( λ,z )= b w ( λ )+ b TSM ( λ,z )
a ph ( λ )= C chla a ph * ( λ )
a g ( λ )= a g ( 440 )exp[ S( λ440 ) ]
a NAP ( λ,z )= C TSM ( z ) a NAP * ( λ ) b TSM ( λ,z )= C TSM ( z ) b TSM * ( λ )
a NAP ( λ )= C TSM,const a NAP * ( λ ) b TSM ( λ )= C TSM,const b TSM * ( λ )
g( λ,z )=exp[ 2 z 0 K d ( λ,z' )dz' ]
g( λ,z )=2 K d ( λ,z )exp[ 2 z 0 K d ( λ,z' )dz' ]
g( λ,z )=2 K TSM 1 κ exp[ 2 z' 0 K TSM ( λ,z' )dz' ]
K TSM ( λ,z )= { a( λ,z )[ αa( λ,z )+β b b ( λ,z ) ] } 1 2
C TSM,ave ( λ )= 0 g( λ,z ) C TSM ( z )dz 0 g( λ,z )dz
p=( κ,α,β )
C TSM,app ( λ )= C TSM,ave ( λ,p )
f p ( p )= i=1 32 ( 1 Δλ λ min λ max | C TSM,app ( λ ) i C TSM,ave ( λ,p, x i ) | 2 dλ ) 1 2 1 Δλ λ min λ max C TSM,app ( λ ) i dλ
p sol = ( k sol , a sol , b sol ) = ( 4.51, 1.08, 3.64 )
C TSM,app ( λ )= C TSM,ave ( λ,x )
f x ( x ) = ( 1 Δ λ λ min λ max | C TSM,app ( λ ) C TSM,ave ( λ , x ) | 2 d λ ) 1 2
d = { [ C bg C bg,ret max ( C bg ) ] 2 + [ C max C max,ret max ( C max ) ] 2 + [ σ σ ret max ( σ ) ] 2 + [ z max z max,ret max ( z max ) ] 2 } 1 2

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