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  • Editor: Christian Seassal
  • Vol. 22, Iss. S3 — May. 5, 2014
  • pp: A947–A959
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Retrieval of vertical particle concentration profiles by optical remote sensing: a model study

Jaime Pitarch, Daniel Odermatt, Marcin Kawka, and Alfred Wüest  »View Author Affiliations


Optics Express, Vol. 22, Issue S3, pp. A947-A959 (2014)
http://dx.doi.org/10.1364/OE.22.00A947


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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

1. Introduction

Inherent optical properties (IOPs) vary with depth in almost all natural waters. In open ocean water, phytoplankton finds a trade-off between stress by UV at the surface, depth-decreasing light availability and depth-increasing nutrient concentrations at the so-called deep chlorophyll maximum [1

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]

4

4. 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]

]. In coastal and inland waters, this feature exists as well for the same reasons [5

5. 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]

], but light availability is in addition affected by other constituents like inorganic particles, which also have inhomogeneous vertical distributions [6

6. 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]

, 7

7. Q. Yang, D. Stramski, and M.-X. He, “Modeling the effects of near-surface plumes of suspended particulate matter on remote-sensing reflectance of coastal waters,” Appl. Opt. 52(3), 359–374 (2013). [CrossRef] [PubMed]

].

Remote-sensing reflectance (Rrs(λ)) is used to retrieve the IOPs and subsequently concentrations of the water’s optically active constituents, usually chlorophyll-a (Cchl-a), dissolved organic matter (quantified by its light absorption at a reference wavelength ag0)) and total suspended matter (CTSM) [8

8. 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]

] and references therein. Rrs(λ) represents a vertically-weighted average of water-leaving radiances across wavelength-dependent penetration depths. But in order to prevent under-determined numerical inversion, vertical homogeneity is usually assumed for the constituent retrieval algorithms. Dissolving this assumption poses a critical challenge for remote sensing, given the ecological significance of the stratification of different water constituents.

The problem of vertical ambiguity means that different vertical distributions of TSM (CTSM(z)) can result in similar surface signals. Contrariwise, each surface signal represents a rough average for different vertical stratifications [9

9. H. R. Gordon, “Remote sensing of optical properties in continuously stratified waters,” Appl. Opt. 17(12), 1893–1897 (1978). [CrossRef] [PubMed]

]. But light penetration depth varies strongly with wavelength, therefore the depth considered in this average varies across the spectral Rrs(λ,Cz). If this variation is properly parameterized, there is a chance to retrieve the vertical structure of the IOPs. Several model studies have showed that Rrs(λ) is sensitive to variations in the vertical structure of the IOPs, like CTSM(z) [6

6. 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]

, 7

7. Q. Yang, D. Stramski, and M.-X. He, “Modeling the effects of near-surface plumes of suspended particulate matter on remote-sensing reflectance of coastal waters,” Appl. Opt. 52(3), 359–374 (2013). [CrossRef] [PubMed]

] and the pigments chlorophyll-a [10

10. M. Stramska and D. Stramski, “Effects of a nonuniform vertical profile of chlorophyll concentration on remote-sensing reflectance of the ocean,” Appl. Opt. 44(9), 1735–1747 (2005). [CrossRef] [PubMed]

] and phycocyanin [11

11. 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]

].

2. Methods

2.1 Construction of the simulated data set

The starting point for our model study is the construction of a simulated data set (SDS) consisting of many pairs of CTSM(z), Rrs(λ,Cz). We arbitrarily consider all TSM profiles CTSM(z) as Gaussian curves:
CTSM(z)=Cbg+Cmaxexp[12(zzmaxσ)2]
(1)
The Gaussian profile depends on four independent parameters, which we vary in discrete steps, according to Table 2.

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

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This scheme leads to 3024 different profiles. The values were chosen for a case study from clear to moderately turbid waters and should be adapted to the range of values to be expected in each real application.

For each CTSM(z), Rrs(λ,Cz) is calculated using the software package Ecolight 5.1.2 [16

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

], which solves the azimuthally-averaged radiative transfer equation in the water given the IOPs and boundary conditions.

Total absorption and scattering are decomposed as:
a(λ,z)=aw(λ)+aph(λ)+ag(λ)+aNAP(λ,z)b(λ,z)=bw(λ)+bTSM(λ,z)
(2)
Absorption aw(λ) and scattering bw(λ) of pure water are parameterized using the measurements of Pope and Fry [17

17. R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

] between 400 nm and 700 nm and those by Smith and Baker [18

18. 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]

] from 700 nm to 800 nm.

Absorption by phytoplankton is modeled as proportional to chlorophyll-a concentration and to a mass-specific spectrum:
aph(λ)=Cchlaaph*(λ)
(3)
As this model study focuses on the retrieval of TSM, we set arbitrarily Cchl-a = 1 µg l−1 and a*ph(λ) being the average of the specific spectra of the five dominant algal species in Lake Constance, as proposed by Gege [13

13. 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.

].

Absorption by dissolved organic substances is modeled by a spectral exponential shape:
ag(λ)=ag(440)exp[S(λ440)]
(4)
We arbitrarily fix the reference absorption ag(440) = 0.2 m−1 and the decay constant S = 0.014 nm−1. Spectral absorption by non-algal particles and scattering by TSM are modeled as proportional to CTSM(z) and the corresponding mass-specific spectra:
aNAP(λ,z)=CTSM(z)aNAP*(λ)bTSM(λ,z)=CTSM(z)bTSM*(λ)
(5)
The mass-specific spectra a*NAP(λ) and b*TSM(λ) are from the brown earth example provided with Ecolight [16

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

], pp. 26-28.

Wavelength band limits are set from 400 nm to 800 nm in steps of δλ = 4 nm (optical bandwidth also 4 nm). The output is averaged for each band and referenced to the central wavelength. All sources of inelastic scattering are considered in the simulation. The quantum yield of fluorescence is set to 0.02. The Raman scattering coefficient is set to 2.6 × 10−4 m−1 at the reference wavelength of 488 nm. The time is set to 25th May 2012, 12 h UTC and the coordinates to 47.52 °N, 9.59 °E (Lake Constance), which results in a sun zenith angle of 28 °. Normalized sky radiances are computed using the sky model of Harrison and Coombes [19

19. 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]

], for an average cloud cover of 0.3. Diffuse and direct sky irradiances are computed using the RADTRANX model, included in the Ecolight software. The clear-sky irradiances are adjusted for cloudiness by the model of Kasten and Czeplak [20

20. 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 parameters are: atmospheric pressure (101,253 Pa), air mass (type 3), relative humidity (80%), precipitable water (2.5 cm), wind speed (4 m s−1), visibility (15 km), ozone concentration (330.1 Dobson units) and aerosol optical thickness (0.261 at 550 nm). The index of refraction of water is calculated for an average water temperature of 14 °C and zero salinity. The water column is considered infinitely deep.

2.2 Construction of the apparent TSM concentrations by spectral matching to a look-up table

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)).
The apparent TSM concentration CTSM,app(λ) is defined as the concentration CTSM,const retrieved from Rrs(λ,Cz) by spectral matching with Rrs(λ,Cconst). Prior to this spectral matching, we construct a look-up table (LUT) for a range of CTSM,const from 0 to 20 mg l−1. We vary CTSM,const in steps of 0.05 mg l−1 (Fig. 1(a)), so that the LUT has 401 elements. The first 25 elements of the LUT for CTSM,const from 0 to 1.2 mg l−1 are plotted in Fig. 1.

Absorption and scattering of TSM are modelled as:
aNAP(λ)=CTSM,constaNAP*(λ)bTSM(λ)=CTSM,constbTSM*(λ)
(6)
The mass-specific spectra a*NAP(λ) and b*TSM(λ) and the rest of IOPs and boundary conditions are set equal as in the SDS. The corresponding Rrs(λ,Cconst) (Fig. 1(b)) are simulated using Ecolight.

2.3 Vertical averaging of a TSM profile

In this section, we present and calibrate a weighting function to vertically average a given profile CTSM(z) and obtain CTSM,ave(λ), with the condition that it matches CTSM,app(λ) as good as possible for every wavelength. Under the assumption of a biunivocal correspondence CTSM(z) ↔ CTSM,ave(λ), the aim is to retrieve CTSM(z) if CTSM,ave(λ) can be determined.

Using the calibrated values of Eq. (15), an excellent match is found between CTSM,app(λ) and CTSM,ave(λ) in this subset (results not shown). However the calibration in Eq. (14) is dependent on the used subset, therefore we must validate the calibration using an independent data set.

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.
The calibrated parameters of Eq. (15) are now applied to a validation data set of another 32 TSM profiles chosen randomly from the SDS. The results (Fig. 2) are very satisfactory and no loss in fitness is observed. Hereafter, we use CTSM,ave(λ) as a proxy for CTSM,app(λ). The reader should note the different scale for each graph. For the cases CTSM,app(λ) is almost constant at a non-zero value, a fluctuating pattern can be appreciated. This error is around five times less than the precision of the LUT, e.g., <0.01 mg l−1 in the worst case we found, which is a negligible difference in real applications. A study in detail of Ecolight’s numerical output showed that the fluctuations come from the numerical precision of Ecolight, whose output reflectances are given to the smallest order of 10−6 sr−1. Another option would be to construct CTSM,app(λ) by taking the nearest element of the LUT instead of linearly interpolating. That would completely eliminate this effect, but would give CTSM,app(λ) a step-wise shape with a precision of 0.05 mg l−1.

2.4 Retrieval of an unknown TSM profile

In this section, we reconstruct CTSM(z) from a given Rrs,Cz). Without loss of applicability for further studies, we suppose here CTSM(z) having an unknown Gaussian shape according to Eq. (1), thereby depending on the four parameters x = (Cbg, Cmax, σ, zmax). Ideally, the aim is to find x so that:
CTSM,app(λ)=CTSM,ave(λ,x)
(16)
Note that, in Eq. (16), we make the dependence of CTSM,ave(λ,x) explicit on x, and omit the dependence on p, since p = psol has been fixed in Eq. (15).

Equation (16) does not have an analytical solution on x, thereby needing a numerical approach. For this sake, we use again GA. Cbg is searched between the bounds 0 and 5 mg l−1, Cmax between 0 and 10 mg l−1, σ between 0 and 3 m and zmax between 0 and 10 m. The number of generations is set to 25 and the population is set to 30. A goal function fx(x) to be minimized is also defined:
fx(x)=(1Δλλminλmax|CTSM,app(λ)CTSM,ave(λ,x)|2dλ)12
(17)
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).
Figure 3 shows how fx(x) (Eq. (17)) is constructed. Based on the established LUT, we estimate the apparent TSM concentration CTSM,app(λ) from a measured Rrs(λ,Cz). Independently, a guess of the Gaussian set x is used to construct a TSM profile, which is vertically averaged by Eq. (11) to obtain CTSM,ave(λ,x). Finally, the goal function is constructed as the Euclidean distance between CTSM,ave(λ,x) and CTSM,app(λ) along the entire λ range. No normalizations are applied in Eq. (17) because zero or near-zero values of CTSM,ave(λ,x) are to be expected for some cases of the SDS.

3. Results and discussion

We perform individual retrievals for each case of SDS. To quantify the performance of our model, we define an error function between the results of our model and the original CTSM(z) profiles (which, in a realistic situation, are not observed) for each case. In our study, all profiles are assumed to be Gaussian, so we define the following non-dimensional distance between the real values and the retrieved (subscript ret):
d={[CbgCbg,retmax(Cbg)]2+[CmaxCmax,retmax(Cmax)]2+[σσretmax(σ)]2+[zmaxzmax,retmax(zmax)]2}12
(18)
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.
The non-dimensional distance d of Eq. (18) increases from zero as the differences between the Gaussian parameters increase. Note that, in a different situation, where CTSM(z) were not Gaussian, the distance d could be defined differently. An option would be a norm between real and retrieved profiles. Figure 4 shows selected original (blue) and retrieved (red) profiles, with the corresponding distance d for each retrieval. By visual inspection of several retrieved profiles, we set the threshold of a good retrieval at d = 0.4. From the plots, the retrievals look excellent if the maximum lays right at the surface (upper panels). However, if the maximum is deep in the water, other factors seem to influence the quality of the retrieval (lower panels).

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.
We study in Fig. 5 which of the Gaussian parameters influence the goodness of the profile retrieval, and what are the interdependencies among them in the subset of the well-retrieved profiles (d < 0.4). Each graph shows, for each value of one of the Gaussian parameters (horizontal axis), the arithmetic mean of the other three parameters in the subset of the SDS that holds the condition d < 0.4. Figure 5(a) illustrates that, although zmax has a mean value for all the SDS of 5 m (cyan, dashed), the retrieval is good (cyan, continuous) only down to a depth of zmax ≈3 m in the best case, which is Cbg = 0 mg l−1. However, as Cbg increases up to 5 mg l−1, zmax decreases down to ~1 m. The explanation is the following: as Cbg increases, light penetration decreases, so that the TSM maximum has to be placed at upper layers so that d can remain lower than 0.4. In contrast, the sensitivity of Cmax to Cbg is weak. The same pattern is observed for σ. In Fig. 5(b), Cmax increases in the horizontal axis. The blue line (Cbg) reveals the same effect as in Fig. 5(a): as Cmax increases, Cbg must decrease, so that d can remain lower than 0.4. The parameter σ remains almost constant and zmax shows not a clear trend. The thickness σ of all profiles increases in the horizontal axis of Fig. 5(c) and variations in the average values of Cbg, Cmax and zmax, are plotted in the vertical axis. As all lines in this graph are fairly horizontal, σ is not a parameter that conditions the success of the retrieval. Last, the depth of the sub-surface maximum zmax is the independent parameter in Fig. 5(d). The strong decrease of Cbg (blue) indicates the explained effect: the deeper the profile is, the clearer the background water has to be so that light reaches the depth where TSM is concentrated.

In summary, Fig. 5 conveys the following conclusions: (1) in average, zmax < 3 m is needed in order to achieve good retrievals in the most favorable cases of clear background water. (2) If condition (1) applies, zmax and Cbg are negatively correlated: as Cbg increases from 0 mg l−1 to 5 mg l−1, zmax decreases on average from 3 m to 1 m. Conversely, as zmax deepens from [0,1] m to [6

6. 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]

,10

10. M. Stramska and D. Stramski, “Effects of a nonuniform vertical profile of chlorophyll concentration on remote-sensing reflectance of the ocean,” Appl. Opt. 44(9), 1735–1747 (2005). [CrossRef] [PubMed]

] m depth, Cbg decreases on average from ~2 to ~0 mg l−1. (3) The quality of the retrieval shows no sensitivity to Cmax and σ.

The reader must note that these numerical results are dependent on the particular IOPs of each case study. We focused on a case study of moderately turbid waters and a certain background chlorophyll-a and CDOM. For the case of cleaner waters, good performance down to greater depths is to be expected. On the contrary, for the case of very turbid surface waters, no vertical information at all can be extracted.

The algorithm’s performance using different numbers of bands is assessed in 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.
We perform the whole procedure explained in this article for different numbers of bands (keeping the optical bandwidth at 4 nm). In black, we show results using all bands available (δλ = 4 nm), whereas the other colors correspond to the three wavelength steps δλ = 12 nm (brown), δλ = 36 nm (red) and δλ = 132 nm (green). Results deteriorate progressively as we use fewer bands, because the information in the shape features of the spectra is lost. However, the effect is not extreme. The spectra evaluated in our algorithm are CTSM,ave(λ) and CTSM,app(λ) (see Fig. 2), whose spectral features are basically the same as of Rrs,Cz), and ultimately, of the IOPs. Our results suggest that for the retrieval of variations in CTSM, a 4 band multispectral sensor has almost the same potential as medium resolution ocean color sensors, provided an equally good radiometric resolution and spectral band characterization. This finding is not transferrable to Cchl-a retrieval, where narrow bands at appropriate wavelengths are crucial.

4. Conclusion

Although light is integrated on its vertical path through the water column, we showed that the vertical structure of a TSM profile leaves signatures in the remote sensing reflectance. Application of this model to our simulated data set showed that the most favorable case for the success of the retrieval is when the TSM profiles have high differences between maximum and background, and when the peak concentrations are close to the surface. The numerical results have to be interpreted for our specific simulated data set, consisting of low to moderate turbid waters with a background chlorophyll-a and CDOM. We do not discard room for further improvements in the method which could increase the sensitivity to deep layers. Besides this, there is always the physical limitation: That is, if the effect of a deeper layer on the water leaving radiance is tiny, that layer is not likely to be detected.

The retrieval of profiles by optical remote sensing is an ambitious and challenging task. Hence limited results are expected if the method is used as standalone. However, we suggest the integration of this model into a scheme of data assimilation of hydrodynamic simulations. Unlike other schemes that assimilate remote sensing products like TSM, this scheme would assimilate the reflectance, which contains the integrated information of the water inherent optical properties. Together with some ancillary data (e.g. the SIOPs) and other source of vertical water quality parameters distribution (e.g. field sampling or ecological modeling) this may lead to reasonably accurate retrieval of the vertical profiles.

A further step would be to address the more difficult problem of the retrieval of several water constituents. However, the success in this approach depends on an accurate knowledge of the IOPs after intensive field and laboratory work, which is also the requirement of physically-based remote sensing algorithms.

Acknowledgments

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 263287 (FRESHMON project). We thank Karin Schenk and Thomas Heege of EOMAP for the management of the project and two anonymous reviewers for their constructive review reports. The first author wants also to thank his new colleagues at ISAC Rome for their interest in this investigation. Their comments and suggestions on both the theoretical development and the practical applicability of this model were incorporated to a revised version of this article.

References and links

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]

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]

3.

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]

4.

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]

5.

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]

6.

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]

7.

Q. Yang, D. Stramski, and M.-X. He, “Modeling the effects of near-surface plumes of suspended particulate matter on remote-sensing reflectance of coastal waters,” Appl. Opt. 52(3), 359–374 (2013). [CrossRef] [PubMed]

8.

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]

9.

H. R. Gordon, “Remote sensing of optical properties in continuously stratified waters,” Appl. Opt. 17(12), 1893–1897 (1978). [CrossRef] [PubMed]

10.

M. Stramska and D. Stramski, “Effects of a nonuniform vertical profile of chlorophyll concentration on remote-sensing reflectance of the ocean,” Appl. Opt. 44(9), 1735–1747 (2005). [CrossRef] [PubMed]

11.

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]

12.

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

13.

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.

14.

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]

15.

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]

16.

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

17.

R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Appl. Opt. 36(33), 8710–8723 (1997). [CrossRef] [PubMed]

18.

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]

19.

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]

20.

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]

21.

H. R. Gordon, “Diffuse reflectance of the ocean: influence of nonuniform phytoplankton pigment profile,” Appl. Opt. 31(12), 2116–2129 (1992). [CrossRef] [PubMed]

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(010.7340) Atmospheric and oceanic optics : Water
(280.0280) Remote sensing and sensors : Remote sensing and sensors

ToC Category:
Remote Sensing and Sensors

History
Original Manuscript: March 6, 2014
Revised Manuscript: April 9, 2014
Manuscript Accepted: April 11, 2014
Published: April 18, 2014

Virtual Issues
Vol. 9, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Jaime Pitarch, Daniel Odermatt, Marcin Kawka, and Alfred Wüest, "Retrieval of vertical particle concentration profiles by optical remote sensing: a model study," Opt. Express 22, A947-A959 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S3-A947


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