OSDOcean Science DiscussionsOSDOcean Sci. Discuss.1812-0822Copernicus GmbHGöttingen, Germany10.5194/osd-12-1893-2015A semi-analytical model for diffuse reflectance in marine and inland watersPravinJ. D.ShanmugamP.pshanmugam@iitm.ac.inAhnY.-H.Ocean Optics and Imaging Laboratory, Department of Ocean Engineering,
Indian Institute of Technology Madras, Chennai, 600036, IndiaKorea Ocean Satellite Research Center, KIOST, Seoul 425-600, KoreaP. Shanmugam (pshanmugam@iitm.ac.in)19August20151241893191215June201522July2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://os.copernicus.org/preprints/12/1893/2015/osd-12-1893-2015.htmlThe full text article is available as a PDF file from https://os.copernicus.org/preprints/12/1893/2015/osd-12-1893-2015.pdf
A semi-analytical model for predicting diffuse reflectance of coastal and
oceanic waters is developed based on the water-column optical properties and
illumination conditions. Diffuse reflectance (R) is an apparent optical
property that is related to the Gordon's parameter
(bb/(a+bb)) through a proportionality factor “f”. The conventional
assumption of “f” as a constant (0.33) yields large errors in case of turbid
and productive coastal waters and a predictive model based on this
assumption is generally restricted to open-ocean waters (low chlorophyll
case). In this paper, we have sorted the dependent factors that influence
“f” values in the water column. Here, the parameter “f” is modeled as
a function of wavelength, depth, inherent optical properties (IOPs) and
illumination conditions. This work eliminates the spectral constants
(KChlandKSS) associated with our previous model and constrains the
present model to be solely dependent on the IOPs and illumination
conditions. Data used for parameterization and validation are obtained from
in situ measurements in different waters within coastal environments. Validation
shows good agreement between the model R and in situ R values with the overall mean
relative error of less than a few percent. The model is valid for a wide
range waters within coastal and open-ocean environments.
Introduction
The significance of reflectance is generally well-known as it is the main
physical quantity that contains the information regarding the seawater
constituents such as phytoplankton, suspended sediments, detrital and
dissolved organic matter (Mobley, 1994; Thomas and Stamnes, 2002).
Reflectance properties of the seawater constituents vary substantially from
one water type to another water type, permitting interpretation of their
existence, nature and composition. Moreover, it is used to analyze the
directional effects (Gordon et al., 1975; Morel and Prieur, 1977), and is
a basic quantity used in remote sensing applications. Reflectance is the ratio
of incoming and outgoing radiant fluxes and hence it has no unit. It varies
between 0 to 1, meaning “0” the complete transmission and “1” the complete
reflection. The reflectance values sometimes go beyond 1 only in the case of
specular reflecting surfaces and in the case of diffuse (Lambertian)
surfaces, values stick equivalent to 1 or even less (Schaepman-Strub et al.,
2006). For natural waters, R values can reach up to at the level of 0.4 (for
hypereutrophic waters). Any contributions from the bottom (floor) or
seagrass can enhance the reflectance considerably. The reflectance spectra
are dependent on the inherent optical properties of the seawater but their
prediction is very complex. In remote sensing applications, optical
properties of the seawater constituents are derived from the reflectance
values through inversion models and remote sensing algorithms (Roesler and
Perry, 1995; Roesler and Boss, 2003; Shanmugam et al., 2010, 2011; Werdell
et al., 2013). Since the reflectance is related to IOPs, the inversion and
remote sensing techniques could produce reliable results only if the
function “f” is determined accurately.
Determination of exact R is not easy (Mobley, 2005), as the factor f is not
a quantity measured directly with a measuring instrument. The prediction of
f is complicated as it depends upon many physical and
environmental/illumination conditions (Dev and Shanmugam, 2014b). Several
researchers have attempted to sort the dependencies of “f” in case 1 waters
(Gordon et al., 1975; Morel and Gentili, 1993; Morel and Prieur, 1977). The
behavior of f in turbid and productive case 2 waters is difficult to predict,
and there is no appropriate and general model reported in the literature.
Albert and Mobley developed an analytical model to predict R based on the
Hydrolight simulations that is limited in case 2 waters (Albert and Mobley,
2003). Though some of the previously published papers show the dependencies
of f on solar angle (Kirk, 1984), wind speed (Albert and Mobley, 2003) and
IOPs (Hirata and Højerslev, 2008; Loisel and Morel, 2001; Morel and
Gentili, 1993; Sathyendranath and Platt, 1997), they do not include
a variety of water conditions within coastal and oceanic environments.
Moreover, models accounting the depth-wise variation of R are scarce (Hirata,
2003; Maritorena et al., 1994). Recently, a realistic model of f was reported
for a variety of water types and operates as a function of the solar zenith
angle, IOPs and wavelength-dependent constants (kChl and kSS) (Dev
and Shanmugam, 2014b). In the present paper, drawbacks of the existing models
that were developed based on radiative transfer simulations are overcome by
the present model, which is solely dependent on the IOPs and illumination
conditions to predict R in coastal and oceanic waters. The
wavelength-dependent constants associated with our previous model are
eliminated by the measured quantities (particularly the IOPs) and hence more
accurate R values are achieved without relying on any assumptions and
wavelength-dependent constants.
In-situ data
In-situ data were collected on several field campaigns in oceanic and turbid
productive coastal waters during May 2012 (Off Point Calimere), August 2013
(Off Chennai), October 2013 (around Chennai coast), November 2013 (Chennai
Harbour), May and November 2013 (Muttukaadu lagoon) (Fig. 1). The above
field locations are optically different regions characterized by waters with
a different composition. Bio-optical measurements were performed on
different coastal research vessels (CRV Sagar Pachimi, CRV Sagar Purvi and BTV Sagar Manjusha) allotted by the National Institute of Ocean Technology (NIOT). The
radiometric measurements included upwelling and downwelling irradiances from
TriOS radiometers and the photometric measurements included absorption and
backscattering coefficients from AC-S and BB9 respectively (Dev and
Shanmugam, 2014a, b). Chlorophyll fluorescence and turbidity were
measured with a FLNTU sensor. Other ancillary data such as temperature,
salinity and conductivity were measured by a CTD sensor.
The nature of water is broadly categorized into five types (based on
chlorophyll and turbidity levels as schematically shown in Dev and
Shanmugam, 2014b): (i) Type I – Clear water (Off Chennai)
(Chl<1mgm-3 and turbidity <1 NTU), (ii) Type II – Relatively clear
water (around Chennai) (1<Chl<3mgm-3 and 1<
turbidity <3 NTU), (iii) Type III – Relatively turbid water
(Chennai Harbour) (5<Chl<25mgm-3 and 1 <
turbidity <3 NTU), (iv) Type IV – Turbid water (Off Point Calimere)
(1<Chl<3mgm-3 and 3< turbidity <14
NTU) and (v) Type V – Productive (eutrophic) water (Muttukaadu lagoon)
(Chl>25mgm-3 and turbidity >5 NTU). Further
details on the data acquisition and processing protocols as well as methods
for laboratory determination of the water constituents can be found
elsewhere (Dev and Shanmugam, 2014a, b; Gokul et al., 2014; Simon and
Shanmugam, 2013; Sundarabalan and Shanmugam, 2015).
Model description
Theoretically, diffuse reflectance (R) is regarded as an apparent optical
property (AOP), which is the ratio of upwelling and downwelling irradiances
(Eq. 1). In the field of marine optics and remote sensing, it can be
calculated analytically from the inherent optical properties (IOP) of the
seawater (Eq. 2 or 3).
R(0-,λ)=Eu(0-,λ)Ed(0-,λ)R(0-,λ)=f(0-,λ)bba+bbR(λ,z)=f(λ,z)bba+bb
Here R is related to the IOPs through a factor “f” (Gordon et al., 1975; Morel
and Prieur, 1977). a and bb denote the absorption and backscattering
coefficients respectively, λ the wavelength, 0- the depth just
below the sea surface, and z the depth layer from the surface. In the
literature, the factor f is generally parameterized based on the assumptions
related to clear oceanic waters and holds very little information of the
other water types in turbid and productive coastal waters. This limits the
possibility of extending such models to predict R in coastal oceanic waters.
In this paper, f is determined just below the water surface and at different
depth levels. As the factor f is dependent partly on the illumination and
environmental conditions, analytic solutions for f predictions are not
possible (Morel and Gentili, 1991, 1993, 1996). Models with restricted
assumptions (such as spectrally invariant, optically homogeneous, zenith sun
angle) lower the accuracy of f and hence degrade the predicted reflectance
values (Sathyendranath and Platt, 1997). However, based on the experiments
conducted in different waters we could provide meaningful interpretation
about this complex f factor.
The spectral variation of f is found to have dependency (Loisel and Morel,
2001) on absorption and backscattering coefficients (Eq. 4), whereas its
magnitude (Sf+If) is dependent on the light field available just
below the sea level. The entire factor f (0-,λ) seems to follow
a power law where its magnitude is the sum of the solar zenith angle function
(Sf) and IOP function (If). Plotting the Sf+If vs.
solar zenith angle (Fig. 2a), the data points seem scattered when they are
shown together for all water conditions. However, it can be closely observed
that the trend followed by each water type is rather consistent although
being shifted relative to each other (i.e., Type I (blue) and II (purple) lie
at the top, Type III (orange) and IV (pink) in the middle, and Type V
(green) at the bottom). Segregating the magnitude term
(Sf+If) provides an insight into the variation of each function
with the solar zenith angle (Fig. 2b and c). The term other than the
solar zenith angle function (Sf) that seems to influence the f factor is
dependent on the IOPs (If). We found the relation between this term
(If) and the inverse of absorption 1/a(400) based on the interpretation of
reflectance properties of different waters. The model requires four inputs
namely the solar zenith angle, Chl concentration, absorption and backscattering
coefficients. The model equation is expressed as follows,
f(0-,λ)=Sf+If⋅bbanf(0-,λ)=0.03⋅exp(0.0462⋅θs)+0.0684⋅1a(400)0.757×bbanwhere,n=0.03×log(Chl)+0.2243.
As shown mathematically in Eq. () and schematically in Fig. 2b and c,
Sf increases exponentially with the increase of solar zenith angle and
If follows a power function which decreases with increasing a(400nm). The
absorption coefficient at 400 nm is chosen because significant variations in
the absorption spectra are evident within this spectral region, whereas at
higher wavelengths the absorption due to the pure seawater dominates.
Consequently both the Sf and If terms determine the magnitude of
f (0-,λ).
Conversely, the term “backscattering by absorption ratio” (bba-1) gives the
spectral character to f (0-,λ). The spectral slope is governed by
the parameter “n”, a function of Chl (Fig. 2d) (Okami et al., 1982). In case
of clear oceanic waters, the spectral slope “n” is small and thereby produces
almost linear f (0-,λ). For productive waters with elevated Chl
concentrations, the slope causes large spectral variations in
f (0-,λ) (Eq. 6). For clear waters (assuming Chl=0.1mgm-3), it takes the value of 0.194 and for turbid productive waters
(Chl=72mgm-3), it takes the value of 0.28 (note that Chl values
presented in this paper refer to FLNTU-measured Chl). Considering all the water
types, the predicted Sf+If values are in excellent agreement with
in situ Sf+If determinations (Fig. 2e).
The depth wise f function [f(λ,z)] is largely dependent on the f just
below the surface [f (0-,λ)]. As noted earlier, the
f (0-,λ) is a function of light field available at just below the
water surface which is approximated on the basis of the solar zenith
function and IOPs. The relation between light fields just beneath the
air–water interface (0-) and the depth z is given by,
f(λ,z)=f(0-,λ)×e-z(Ku-Kd)R(λ,z)=f(λ,z)bba+bbR(λ,z)=f(0-,λ)bba+bb×e-(Ku-Kd)z
where f (0-,λ) is from Eq. (5). In case, if the oceanic system is
homogeneous, R throughout the water column must be uniform without any
fluctuations. This in turn sheds light on the f function of both 0- and
z. For the uniform R throughout the vertical column, R (0-,λ) must
be equivalent to R(λ,z). Since most of the natural waters are
non-homogeneous (because the water constituents are in general not
homogeneously distributed) the fluctuations of R are expected. The
fluctuations in R are replicated on the f. Since f is a function of light field
available in the water column, it tends to decrease with depth as denoted by
–z (minus z) in Eq. (7). The term (Ku-Kd) is the change in the upwelling
and downwelling diffuse attenuation coefficients that induce the
corresponding change (increase or decrease) in f(λ,z). Thus, any
underwater fluctuations in R depend on the change in the upwelling and
downwelling diffuse attenuation coefficients (Eqs. 7 and 8).
Results and discussion
For evaluating the performance of the present model, the underwater diffuse
reflectance profiles for the considered five water bodies were modeled based
on the measured IOPs (absorption and backscattering) and the derived
f(λ,z) and (Ku-Kd) values. The model R values were then compared
with those determined from in situ measurements of upwelling and downwelling
irradiances. Figure 3a1–e2 shows the comparison of model-derived
and measured reflectances for each water types (Type-I to Type-V), wherein
the black line represents the measured R and the orange line represents the
simulated R. Two examples from each water type are presented (in column
wise). The sub-plots labeled as a, b, c, d and e correspond to the water Types I
to V respectively and the subscripts 1 and 2 represent two different
stations for a particular water type. The R spectra of each water type
(ranging from clear to turbid) are unique and distinct from each other in
its spectral shape. Figure 3a1 and a2 represents the clear oceanic
Type-I waters with very low chlorophyll concentration (<0.25mgm-3) and low turbidity (<0.6 NTU). The presence of very low
seawater contents diminishes the absorption coefficient in the blue region
that subsequently gives high reflectance in this spectral region. At higher
wavelengths, high absorption and low backscattering produce very low
reflectance tending close to zero. The model is able to produce the R spectra
similar to the in situ R spectra. Figure 3b1 and b2 represents the
relatively clear Type-II waters with Chl concentration and turbidity less than
2 mgm-3 and 2 NTU. Here, the absorption coefficient is comparatively
higher than that of Type-I waters that diminishes the magnitude of the
reflectance in the blue region. This is clearly seen with the primary peak
shifting from the blue region (Type 1 case) to the green region (around
500–550 nm) due to the absorption effect. Though the Chl concentration at these
stations is greater than 1 mgm-3, the secondary peak (around 685 nm)
is not well pronounced due to the considerable amount of suspended sediments
(that increased turbidity level from 1.4–2 NTU). The considerable amount
of suspended sediments enhances backscattering at higher wavelengths
(650–700 nm), resulting in non-zero reflectance spectra. The reflectance
spectra predicted by the model agree well with the in situ measurements.
In Type-III waters with Chl nearly five times greater than its turbidity level,
chlorophyll (and of course, other constituents such as colored dissolved
substance and non-algal particles) absorbs light strongly in the blue
portion, further diminishing the reflectance spectra below 0.01
(Fig. 3c1 and c2). The reflectance spectra predicted by the model are
consistent with the in situ spectra, wherein both the primary and secondary peaks
are well pronounced because of the elevated Chl concentration and reduced
turbidity.
The Type-IV waters are dominated by suspended sediments and little
chlorophyll in contrast to the Type-III waters. The turbidity level at these
two stations (Fig. 3d1 and d2) is greater than 5 NTU, while the
Chl concentration remains low (<2mgm-3). At these stations,
high backscattering by suspended sediment particles is particularly effected
in the NIR region and hence the enhanced R values when compared to the
previous cases (Types I, II and III). As a consequence, the secondary peak
around 685 nm is suppressed because of the elevated suspended sediment
concentration relative to the Chl concentration. The absorption effect of algal
and non-algal particles is seen as the reduced R in the blue part of the
spectrum. The model remains stable and consistent in terms of reproducing
the measured R spectra.
The applicability of this model is also verified in turbid productive
(eutrophic) waters characterized by very high turbidity (>7 NTU)
and Chl (44 mgm-3). The typical R spectra from these waters are shown in
Fig. 3e1 and e2, wherein the primary peak is further shifted toward
the yellow spectral region and the secondary peak toward the NIR region. The
combined effect of both backscattering and fluorescence/absorption tends to
cause a reflectance peak at NIR (Ahn and Shanmugam, 2007; Dev and Shanmugam,
2014a; Shanmugam et al., 2013). The absorption by phytoplankton, non-algal
particles and dissolved substance is abnormally high so that the R values
approach near-zero (<0.005) in the blue region. Notably, the
predicted R spectra agree well with the measured R spectra despite the slight
discrepancy in the red portion.
The consistency of the model to predict the vertical profiles of reflectance
is further investigated. Figure 4a and b displays the variation of R
throughout the water column. For brevity, the results are shown only for two
stations – one from turbid coastal water off Point Calimere (Fig. 4a) and
the other from Chennai Harbour water (Fig. 4b). Two examples are chosen
randomly to show the closeness of the model results with measurements. Since
the water constituents are not homogeneously distributed with depth in these
water bodies, R cannot be constant throughout the water column and can either
increase or decrease vertically depending on the constituents present in it
(Hirata, 2003). Fluctuations in R(λ,z) can be accurately predicted by
the exponential term “Ku-Kd” in Eq. (8). If Ku>Kd, R decreases and
if Ku<Kd, R increases. This behavior of R has been discussed in Dev and
Shanmugam (2014b). As shown in Fig. 5, the agreement between the model and
measured R values is generally good in each case and they consistently
acknowledge the increasing and decreasing trends throughout the water
column. These results confirm that the model is capable of accurately
predicting spectral and vertical distributions of R in different waters
within coastal environments.
Further statistical analysis performed on the spectral and vertical R profile
data from the model and measurements (Table 1) demonstrates significantly
lower errors (RMSE ≤21.4 %; MRE ≤5.8; Bias ≤0.053) and higher slope and R2 values. The one-to-one
correspondence with small errors across the entire visible region and depth
levels confirms the validity of the present model in a wide range of
conditions within coastal environments.
Comparing the present model with existing models, it should be noted that
the existing are designed with certain assumptions to predict R in case 1
waters or coastal (case 2) waters. For instance, a model that is originally
developed for clear oceanic case 1 waters (Gordon et al., 1975; Morel and
Prieur, 1977; Kirk, 1984) gives biased reflectance values in turbid coastal
and productive water types. A model of case 2 waters (Albert and Mobley,
2003) is found restricted to case 2 waters (Dev and Shanmugam, 2014b). In
contrast, the present model is purely based on the analytical and
experimental results, and is well suited for a wide range of waters within
open-ocean and coastal environments. The inter-comparison of the results
from this model and existing models is not shown in this work for brevity.
Conclusion
A semi-analytical model has been developed to predict the spectral and
vertical profiles of diffuse reflectance in coastal oceanic waters. The
model results were validated with measurement data from a wide variety of
coastal and open ocean waters. The model proves to be efficient in terms of
reproducing these in situ data from five water types with the desired accuracy.
This model overcomes the limitations associated with existing models and
predicts R as a function of IOPs and illumination conditions. The present
model is applicable to homogenous, inhomogeneous as well as stratified
waters. It is anticipated that it will have great significance in hydrologic
optics, remote sensing studies, underwater imaging and related engineering
applications.
Acknowledgement
This research was supported by INCOIS under the grant (OEC1314117INCOPSHA) of
the SATCORE program. The work was partly supported by the Korea Ocean
Satellite Centre, Korea Institute of Ocean Science and Technology (KIOST)
through support from the Korean Federation of Science and Technology
Societies (KOFST), Korea. We would like to thank D. Rajasekhar, The Head,
Vessel Management Cell (VMC), and Director of National Institute of Ocean
Technology (NIOT) for providing the CRV Sagar Purvi,
CRV Sagar Pachimi and BTV Sagar Manjusha (Coastal Research
Vessels) to Indian Institute of Technology (IIT) Madras, Chennai, India. We
are thankful to the Topical Editor, Mario Hoppema, for providing valuable
comments to improve the quality of this manuscript.
ReferencesAhn, Y.-H. and Shanmugam, P.: Derivation and analysis of the fluorescence
algorithms to estimate phytoplankton pigment concentrations in optically
complex coastal waters, J. Opt. A-Pure Appl. Op., 9, 352–362,
doi:10.1088/1464-4258/9/4/008, 2007.Albert, A. and Mobley, C. D.: An analytical model for subsurface irradiance
and remote sensing reflectance in deep and shallow case-2 waters, Opt.
Express, 11, 2873–2890, 10.1364/OE.11.002873, 2003.Dev, P. J. and Shanmugam, P.: A new theory and its application to remove the effect of surface-reflected light in above-surface radiance data from clear and turbid waters, J. Quant. Spectrosc. Ra., 142, 75–92,
doi:10.1016/j.jqsrt.2014.03.021, 2014a.Dev, P. J. and Shanmugam, P.: New model for subsurface irradiance reflectance in clear and turbid waters, Opt. Express, 22, 9548–9566,
doi:10.1364/OE.22.009548, 2014b.Gokul, E. A., Shanmugam, P., Sundarabalan, B., Sahay, A., and Chauhan, P.: Modelling the inherent optical properties and estimating the constituents' concentrations in turbid and eutrophic waters, Cont. Shelf Res., 84, 120–138,
doi:10.1016/j.csr.2014.05.013, 2014.
Gordon, H. R., Brown, O. B., and Jacobs, M. M.: Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean, Appl. Opt., 14, 417–27, 1975.
Hirata, T.: Irradiance inversion theory to retrieve volume scattering function of seawater, Appl. Opt., 42, 1564–73, 2003.Hirata, T. and Højerslev, N. K.: Relationship between the
irradiance reflectance and inherent optical properties of seawater, J. Geophys. Res., 113, C03030,
doi:10.1029/2007JC004325, 2008.Kirk, J. T. O.: Dependence of relationship between inherent and apparent optical properties of water on solar altitude, Limnol. Oceanogr., 29, 350–356,
doi:10.4319/lo.1984.29.2.0350, 1984.
Loisel, H. and Morel, A.: Non-isotropy of the upward radiance eld in typical coastal (Case 2) waters, Int. J. Remote Sens., 22, 275–295, 2001.Maritorena, S., Morel, A., and Gentili, B.: Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo, Limnol. Oceanogr., 39, 1689–1703,
doi:10.4319/lo.1994.39.7.1689, 1994.
Mobley, C. D.: Light and Water: Radiative Transfer in Natural Waters, Academic Press, Inc., San Diego, 1994.
Mobley, C. D.: Informal Notes on Reflectances, Sequoia Scientific, Inc, Bellevue, WA 98005, 2005.
Morel, A. and Gentili, B.: Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution, Appl. Opt., 30, 4427–4438, 1991.
Morel, A. and Gentili, B.: Diffuse reflectance of oceanic waters. II. Bidirectional aspects, Appl. Opt., 32, 6864–6879, 1993.
Morel, A. and Gentili, B.: Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem, Appl. Opt., 35, 4850–4862, 1996.Morel, A. and Prieur, L.: Analysis of variations in ocean color, Limnol. Oceanogr., 22, 709–722,
doi:10.4319/lo.1977.22.4.0709, 1977.
Okami, N., Kishino, M., Sugihara, S., and Unoki, S.: Analysis of ocean color spectra (I) – calculation of irradiance reflectance, J. Oceanogr. Soc. Japan, 38, 208–214, 1982.Roesler, C. S. and Boss, E.: Spectral beam attenuation coefficient retrieved from ocean color inversion, Geophys. Res. Lett., 30, 1468,
doi:10.1029/2002GL016185, 2003.Roesler, C. S. and Perry, M. J.: In situ phytoplankton absorption, fluorescence emission, and particulate backscattering spectra determined from reflectance, J. Geophys. Res., 100, 13279–13294,
doi:10.1029/95JC02176, 1995.
Sathyendranath, S. and Platt, T.: Analytic model of ocean color, Appl. Opt., 36, 2620–2629, 1997.Schaepman-Strub, G., Schaepman, M. E., Painter, T. H., Dangel, S., and Martonchik, J. V.: Reflectance quantities in optical remote sensing – definitions and case studies, Remote Sens. Environ., 103, 27–42,
doi:10.1016/j.rse.2006.03.002, 2006.
Shanmugam, P., Ahn, Y.-H., Ryu, J.-H., and Sundarabalan, B.: An evaluation of inversion models for retrieval of inherent optical properties from ocean color in coastal and open sea waters around Korea, J. Oceanogr., 66, 815–830, 2010.Shanmugam, P., Sundarabalan, B., Ahn, Y.-H., and Ryu, J.-H.: A New Inversion Model to Retrieve the Particulate Backscattering in Coastal/Ocean Waters, IEEE T. Geosci. Remote, 49, 2463–2475,
doi:10.1109/TGRS.2010.2103947, 2011.
Shanmugam, P., Suresh, M., and Sundarabalan, B.: OSABT: An innovative
algorithm to detect and characterize ocean surface algal blooms, IEEE J. Sel.
Top. Appl., 6, 1879–1892, 2013.Simon, A. and Shanmugam, P.: A new model for the vertical spectral diffuse attenuation coefficient of downwelling irradiance in turbid coastal waters: validation with in situ measurements, Opt. Express, 21, 30082,
doi:10.1364/OE.21.030082, 2013.Sundarabalan, B. and Shanmugam, P.: Modelling of underwater light fields in turbid and eutrophic waters: application and validation with experimental data, Ocean Sci., 11, 33–52,
doi:10.5194/os-11-33-2015, 2015.
Thomas, G. E. and Stamnes, K.: Radiative Transfer in the Atmosphere and
Ocean, Cambridge University Press, 73–77, 2002.Werdell, P. J., Franz, B. A., Bailey, S. W., Feldman, G. C., Boss, E., Brando, V. E., Dowell, M., Hirata, T., Lavender, S. J., Lee, Z., Loisel, H., Maritorena, S., Mélin, F., Moore, T. S., Smyth, T. J.,
Antoine, D., Devred, E., d'Andon, O. H. F., and Mangin, A.: Generalized ocean color inversion model for retrieving marine inherent optical properties, Appl. Opt., 52, 2019–2037,
doi:10.1364/AO.52.002019, 2013.
Statistical comparison of the model and in situ R for five types of
waters.
(a) Study sites on the southeast part of India (shown in red box).
(b) Magnified study area covering Chennai, Muttukadu and Point Calimere. (c)
Magnified study area with stations covering Chennai (Type I, II, and III)
and productive Muttukaadu lagoon system (Type V).
Scatter plots showing dependencies of (a and b) Sf on the solar
zenith angle, (c)If on the 1/a(400), (d) Chl on the spectral slope parameter
“n” and (e)1:1 correspondence of model and in situ Sf and If.
Comparison of the modeled R (orange line) and measured R (black line)
from different waters.
Vertical profiles of the modeled and measured R from for two coastal
waters sites (results shown for some key wavelengths). Bold lines represent
the measured R and the dotted lines represent the model R.
Scatter plots comparing the model R and in situ R from all five types of
waters and depth levels (results shown for some key wavelengths: 412, 448,
488, 531, 555, 670, 685 and 710 nm).