Advances in Remote Sensing, 2012, 1, 19-34
http://dx.doi.org/10.4236/ars.2012.12003 Published Online September 2012 (http://www.SciRP.org/journal/ars)
An Optical Model for the Remote-Sensing of Absorption
Coefficients of Phytoplankton in Oceanic/Coastal Waters
Surya Prakash Tiwari, Palanisamy Shanmugam
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, India
Email: pshanmugam@iitm.ac.in
Received July 2, 2012; revised July 31, 2012; accepted August 20, 2012
ABSTRACT
A new model for the remote sensing of absorption coefficients of phytoplankton aph(λ) in oceanic and coastal waters is
developed and tested with SeaWiFS and MODIS-Aqua data. The model is derived from a relationship of the remote
sensing reflectance ratio Rrs(670)/Rrs(490) and aph(λ) (from large in-situ data sets). When compared with over 470 inde-
pendent in-situ data sets, the model provides accurate retrievals of the aph(λ) across the visible spectrum, with mean
relative error less than 8%, slope close to unity and R2 greater than 0.8. Further comparison of the SeaWiFS-derived
aph(λ) with in-situ aph(λ) values gives similar and consistent results. The model when used for analysis of MODIS-Aqua
imagery, provides more realistic values of the phytoplankton absorption coefficients capturing spatial structures of the
massive algal blooms in surface waters of the Arabian Sea. These results demonstrate that the new algorithm works well
for both the coastal and open ocean waters observed and suggest a potential of using remote sensing to provide knowl-
edge on the shape of phytoplankton absorption spectra that are a requirement in many inverse models to estimate
phytoplankton pigment concentrations and for input into bio-optical models that predict carbon fixation rates for the
global ocean.
Keywords: Remote Sensing; Phytoplankton Absorption; Bio-Optical Models; Coastal Waters; MODIS-Aqua;
SeaWiFS; Arabian Sea
1. Introduction
Phytoplanktons play a critical role in the cycling of bio-
geochemical properties, and are responsible for much of
the oxygen present in the Earth’s atmosphere through a
process known as photosynthesis. Their cumulative en-
ergy fixation in carbon compounds that account for ap-
proximately half of the world’s total primary productivity
is the basis for the majority of oceanic food chains. They
are highly diverse in shape, size, and pigmentation, hav-
ing a predominant influence on the colour of seawater
measured by satellite sensors [1,2].
Light absorption by particulate phytoplankton—which
determines the amount of radiant energy captured by them
—is an important source of optical variability in surface
waters of the ocean. This variability has consequences
for light attenuation, primary production, remote sensing
of pigment biomass and mixed layer heating [3-8]. The
spectra of phytoplankton absorption (aph(λ)) vary widely
both in terms of magnitude and spectral behaviour [9-11]
in seawaters because of differences in phytoplankton
community, cell size, and pigment packages among sites
[11-13]. For these reasons and because of the advent of
remote sensing capabilities, there is increasing demand
for a fundamental knowledge of the magnitude, range
and sources of variability in phytoplankton optical prop-
erties in marine surface waters. Remote sensing offers the
potential for synoptic assessment of pigment biomass and
primary production, but this requires the ability to accu-
rately estimate phytoplankton absorption coefficients from
remotely measured signals using an appropriate optical
model that has potential applications in ocean colour
remote sensing.
To estimate aph(λ) coefficients from remote sensing
data, several models have been reported in the recent stud-
ies which enable retrieval of two or more in-water con-
stituents and properties simultaneously. For these models,
an inversion technique is usually applied to a parameter-
ized ocean colour model whose parameters have been
determined from in-situ bio-optical measurements. Garver
and Siegel [14] developed a nonlinear statistical method
for the inversion of ocean colour data, which assumed
the known spectral shapes of specific absorption coeffi-
cients for phytoplankton. Later, this model was improved
and optimized by Maritorena et al. [15] (the GSM01
model) using simulated annealing, thus the model could
be applied to global ocean colour data for improved re-
trievals of pigment concentrations. However, GSM model
provides absorption coefficients of phytoplankton at spe-
C
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S. P. TIWARI, P. SHANMUGAM
20
cific wavelengths. Lee et al. [16] developed a multiband
quasi-analytical model (QAA) based on the relationships
between remote sensing reflectance and IOPs of water
derived from the radiative transfer equation. Though the
QAA model provides aph(λ) within ~15% of the input
values [16] in open ocean waters, it yields aph values at
specific wavelengths in the blue-green domain and sig-
nificantly large errors (> 27%) in coastal waters [17].
Smyth et al. (2006) developed a semi-analytical model to
the problem of determining inherent optical properties
(IOPs) from satellite and in-situ ocean colour data. This
model has the same limitations as other models produc-
ing large errors particularly at 555 nm (see Figure 5 in
Smyth et al. [18]). Boss and Roesler [19] developed a
constrained linear matrix inversion model with statistical
selection to obtain absorption coefficients of phytoplankton
and other IOPs from the ocean radiance. An evaluation
of these models in a recent study from coastal waters
indicated that the spectrum of aph(λ) is currently obtain-
able for only few wavelengths within the blue-green do-
main; this causes the main difficulty in making the mo-
dev id="pf7" class="pf w0 h0" data-page-no="7">
S. P. TIWARI, P. SHANMUGAM 25
Figure 3. Scatter plots between the Carder in-situ and model aph(443) and aph(670) versus chlorophyll concentrations.
Table 2. Statistical comparison between the modeled and in-situ datasets (SeaWiFS, Carder, and NOMAD-2). RMSE, MRE,
and MNB and linear-regression results of the datasets at 412, 443, 490, 510, 530, 555, 670, and 683 nm are also presented.
IOPs RMSE MRE (%) MNB SLOPE INTERCEPT R2 N
NOMAD-2 In situ Data Set
aph(412) 0.2387 8.06 0.0795 1.02 0.1011 0.8572 470
aph(443) 0.2038 4.95 0.0475 1.009 0.0567 0.8777 470
aph(490) 0.2321 6.27 0.0716 1.048 0.1305 0.8596 470
aph(510) 0.2408 5.17 0.0683 1.034 0.1148 0.8682 470
aph(555) 0.3038 6.03 0.1044 0.9427 –0.0008 0.8279 470
aph(670) 0.2552 –5.27 –0.0814 0.9534 –0.1496 0.8881 470
aph(683) 0.2802 –4.25 –0.0704 0.9354 –0.1728 0.8747 470
Average 0.2507 2.994 0.0314 0.9918 0.0114 0.8648 470
Carder In situ Data Set
aph(412) 0.1904 5.14 0.0718 0.8123 –0.2039 0.8481 477
aph(443) 0.1847 5.01 0.0677 0.8008 –0.2148 0.8443 477
aph(490) 0.1919 4.66 0.072 0.7977 –0.2551 0.8453 477
aph(510) 0.216 5.05 0.0889 0.8081 –0.266 0.8491 477
aph(555) 0.2912 5.61 0.1237 0.7847 –0.3779 0.8196 477
aph(675) 0.2461 –2.21 –0.0466 0.8834 –0.2866 0.8291 477
Average 0.22 3.877 0.0629 0.8145 0.2674 0.8393 477
NOMAD SeaWiFS Satellite-Matchups Data Set
aph(412) 0.2135 6.24 0.0912 0.7702 –0.2657 0.7952 102
aph(443) 0.2029 4.91 0.0694 0.74 –0.3165 0.7993 102
aph(490) 0.2174 5.15 0.0829 0.7403 –0.3566 0.7855 102
aph(510) 0.2416 5.38 0.0987 0.7497 –0.3847 0.7979 102
aph(530) 0.2894 6.91 0.1422 0.7468 –0.4149 0.7948 102
aph(555) 0.3462 8.29 0.1902 0.7188 –0.5084 0.7745 102
aph(670) 0.2932 1.09 0.0231 0.7175 –0.5832 0.7848 102
aph(683) 0.3304 2.17 0.0493 0.69 –0.6697 0.7748 102
Average 0.2668 5.018 0.0934 0.7342 –0.4375 0.7884 102
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S. P. TIWARI, P. SHANMUGAM
Copyright © ARS
26
the wavelengths from 412 nm - 683 nm, producing low
statistical errors (RMSE 0.2038 - 0. 3038 with an av-
erage of 0.2507, MRE—5.270% - 8.06% with an aver-
age of ~3.0 %, slope 0.935 - 1.048, R2 0.8279 - 0.888,
intercept values——0.172 - 0.13). These results confirm
that the aph(λ) predicted by the model at all these wave-
lengths matched closely with their corresponding in-situ
aph(λ) values very well, although slightly deviating from
linearity at the higher end which may be due to prob-
lems with the in-situ data sampling techniques.
wide range of coastal and oceanic waters were used to
assess the performance of the new model. Figure 5
compares the model estimates of aph(λ) with the in-situ
measurements of aph(λ). The statistical results are sum-
marized in Table 2 for all the selected wavelengths from
412 to 683 nm. Note that the model aph(λ) values show
very good agreement with in-situ aph(λ) coefficient val-
ues at 412, 443, 490, 555, and 670 nm, with low statistic-
cal errors (RMSE 0.184 - 0. 291 with an average of 0.22,
MRE—2.21% - 5.14% with an average of ~3.87%, slope
0.784 - 0.883, R2 0.819 - 0.849, intercept values –0.203 -
–0.377). Compared with the previous validation, the
RMSE is low, but other statistics become slightly worse.
4.1.2. Comparison with Carder In-Situ Dat a Set
The in-situ aph(λ) made by Carder and his colleagues in a
Figure 4. Comparison of modelled aph(λ) with in-situ data taken from the NOMAD-2 database at wavelengths from 412 to 683
(N = 470).
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S. P. TIWARI, P. SHANMUGAM 27
However, the scatters of data are closely aligned with the
1:1 line indicating the validity of the model.
4.1.3. Comparison with SeaWiFS Satellite Data Set
A validation of the model was also performed by com-
paring satellite (SeaWiFS) estimates of aph(λ) with con-
current in-situ aph(λ) measurements. Figure 6 shows the
scatter plots of the predicted aph(λ) values versus the
in-situ values. Table 2 presents the statistical analysis
results at the wavelengths from 412 to 683 nm. When
applied to the SeaWiFS match-up remote sensing reflec-
tance, it can be seen that the aph(λ) values from the model
closely agree with the in-situ data, without much scatters
above or below the 1:1 line. The good agreement be-
tween these data sets can also be observed in Table 2
(RMSE 0.202 - 0. 34 with an average of 0.26, MRE
1.09% - 8.29% with an average of ~5.01%), slope 0.69 -
0.77, R2 0.774 - 0.797, and intercept values –0.66 -
–0.26). Although these errors are slightly higher than
those observed with the previous data sets, the model
still produced the observed aph(λ) values and resulted in
low statistical errors. These results clearly indicate that
the new model has the potential to retrieve accurately the
aph(λ) values in both clear and turbid coastal waters, and
would be useful for applications with remote sensing
data in these waters.
4.1.4. Error Plots
Figure 7 provides greater clarity in the variations of
MRE between the derived and in-situ values of aph(λ) at
412 nm - 683 nm. Though the MRE values for the new
model are notably small at all wavelengths for the three
independent data sets, it shows a significant variability
across these wavelengths. For the NOMAD-2 data set,
the MRE value is high at 412 nm (~8.06%), and gradu-
ally decreases towards the longer wavelengths. By con-
trast, for the Carder and SeaWiFS match-up data sets, the
MRE values are low in the blue wavelengths, increasing
at the green wavelengths and sharply decreasing towards
the longer wavelengths. However, these values are still in
Figure 5. Comparison of modelled aph(λ) with in-situ data taken from the Carder database at wavelengths from 412 to 675 (N
= 477).
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S. P. TIWARI, P. SHANMUGAM
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Figure 6. Comparisons of the modelled aph(λ) with those from the in-situ dataset (NOMAD SeaWiFS match-ups dataset) at
the wavelengths from 412 to 683 nm (N = 102).
the acceptable range as far as the aph(λ) modeling is con-
cerned, because the current models produce very high
errors in moderately turbid to highly turbid coastal wa-
ters [28].
4.2. Application to Satellite Ocean Colour Data
To further assess the efficiency of the new aph model, the
MODIS-Aqua Level 1A (~1 km/pixel at nadir) imagery
acquired over bloomed waters of the Arabian Sea on 18
February 2010, was processed using a regional Complex
water Atmospheric correction Algorithm Scheme (CAAS)
[27] to avoid known issues with the SeaDAS atmos-
pheric correction algorithm in these waters. Subsequently,
the proposed model was applied to the atmospherically
corrected imagery to envisage the phytoplankton absorp-
tion coefficients at 443 and 670 nm. Figure 8(a) and
Figure 8(b) show the regional distribution patterns of aph
(443) and aph(670) in the Arabian Sea. As expected, the
distribution patterns illustrate the influence of coastal waters
on the phytoplankton absorption coefficients across the
entire Arabian Sea during 18 Feb. 2010. Figure 8(c) pre-
sents an example of aph spectra from this new model us-
ing the same MODIS-Aqua data, which typically have
two peaks (same as the measured aph spectra) around 443
and 670 nm. There is relatively lower absorption between
550 and 650 nm. These peaks and troughs are essentially
due to the presence of Chl pigment. The width of the
peaks around 443 and 670nm varies from sample to sam-
ple, due to the change in accessory pigments present and
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S. P. TIWARI, P. SHANMUGAM 29
Figure 7. MRE between the derived and the in-situ values of coefficients of absorption by phytoplankton aph(λ) for the new
model.
the “package effect” [29-33]. These results indicate that
the spectral variations of the phytoplankton absorption
are reasonably good, both in terms of the spectral shape
and magnitude in the visible wavelengths domain.
This satellite imagery was selected as a good example to
address the atmospheric correction related issues. Figure
9(a) displays a typical distribution of sun glint measured
at 551 nm and confirms that the glint contaminated por-
tion of the image extends across the bloomed region in
the central Arabian Sea. It is apparent that the density of
mineral aerosol (desert) dust is not uniform, and it is very
strong in the vicinity of desert coasts and across the Ara-
bian Sea. The corresponding true colour composite (Band
253) for this area which was atmospherically corrected
by the CAAS algorithm removes all these effects (Figure
9(b)). One of the typical problems with the SeaDAS at-
mospheric correction algorithm is that it produces nega-
tive water-leaving radiance (Lw) values in optically com-
plex waters (containing plumes and blooms). This prob-
lem is clearly seen in Figure 9(c), where the SeaDAS
algorithm often rendered negative Lw in the blue, or cre-
ated a cloud or a complete atmospheric correction failure
because of the elevated NIR radiances. Most of the sur-
face algal blooms present always non-zero values at the
NIR bands and near-zero values (sometime negatives) at
the short-wavelengths bands (e.g. 412 nm). It is clear that
the spectral curvatures between 488 and 551 nm are re-
tained in the SeaDAS Lw during the low bloom condition.
However, the curvatures are not present in the Lw spectra
(i.e. large distortions in Lw structures with high negative
values across the wavebands) during the high bloom
(surface) condition. The dramatic anomalous negative Lw
values could be attributed to the black-pixel assumption
or inadequacy of the NIR correction scheme with the
SeaDAS algorithm [27]. By contrast, the CAAS-derived
Lw are more realistic depicting the different stages of
algal blooms, with the presence of a red edge in the NIR
which is indicative of the dense mats of floating phyto-
plankton similar to land vegetation.
4.3. Implications for the Optical Remote Sensing
Changes in the concentration and composition of the water
constituents, due to biological, chemical or physical proc-
esses, affect light penetration in the water and the spec-
tral signature of light that leaves the water surface. In
open ocean waters (Case-1 type), which are usually deep
and free of terrestrial influence, variations in optical prop-
erties are linked to phytoplankton and their by-products.
These are major constituents affecting changes in the
spectral signature of water-leaving radiance. In Case 2
waters, which include most coastal regions, the concen-
trations of the optically significant constituents can vary
independently of each other. Interpreting optical remote
sensing signals from such waters is particularly chal-
lenging [34,35], as it can be seen with the standard algo-
rithms frequently producing erroneous results. The prob-
lem is amplified by the fact that the atmospheric correc-
tion algorithms used for marine remote sensing assume
zero reflectance in the near infra-red, which is not valid
for turbid waters. However, the knowledge and under-
standing of phytoplankton absorption coefficients are lim-
ited by the present algorithms, although these data have
significant effects on global bio-product in the ocean and
to the carbon cycle. Therefore, obtaining the spectral
absorption coefficients aph(λ) of phytoplankton on a re-
gional and global scale is important for studies on the
ocean’s role in the global biological production, carbon
cycle and climate change [36]. In order to use ocean-colour
measurements to derive information on the concentration
and composition of optically active substances in the
water, it is necessary to develop bio-optical algorithms
that relate the water-leaving radiance to the optical prop-
erties of the substances present in the water. The deter-
mination of bio-geo-physica parameters, such as chlo- l
Copyright © 2012 SciRes. ARS
S. P. TIWARI, P. SHANMUGAM
30
Figure 8. (a,b) MODIS/AQUA data for 18th February 2010 over Arabian Sea, showing the model implementation for the
fields of aph(443) and aph(670), (c) aph spectra obtained using the CAAS estimated reflectance values.
rophyll concentration, based on water-leaving radiances,
is relatively less complex for Case 1 waters where the
spectral signature of the emerging light is mostly affected
by phytoplankton and their by-products. The situation is
very different in Case 2 coastal and estuarine waters that
are characterized by higher optical and biological com-
plexity, since other substances such as detritus, mineral
particles, dissolved organic and inorganic material, also
affect the light signal measured by the satellite sensor.
The new aph(λ) model when applied with the CAAS al-
gorithm particularly provides more reliable aph products
for coastal and estuarine waters.
5. Discussion
Though a wide variety of models-with varying degrees of
complexity ranging from empirical to complex semi
-analytical approaches-for determination of the aph(λ)
coefficients were developed in the past, no models have
the potential to provide reliable aph(λ) products in coastal
waters. Thus, accurate estimation of aph(λ) in these wa-
ters is still a daunting challenge. Hoge et al. [37,38]
found that aph(λ) products at the wavelengths of 490, 510
and 555 nm are often estimated with large errors, when
derived from a linear matrix inversion model. In another
study, aph(675) was obtained by an inversion model us-
ing the spectral remote sensing reflectance ratio between
412:443 and 443:551, which assumed the values of sev-
eral algebraic constraints [30]. aph(675) values were de-
termined by fitting a hyperbolic tangent function to
aph(675) and defaulted to an empirical band ratio algo-
rithm when solution was not reached. Many other reflec-
tance-based models (inversion models) are also available
in the literature such as QAA, LM, and GSM [19].
However, these models are applicable only in clear oce-
anic waters, and provide no aph data at the longer wave-
lengths (in the red domain). This could be because of the
fact that the total absorption coefficient is generally
dominated by pure seawater in oceanic waters, except for
eutrophic waters when aph(λ) makes significant contribu-
tions to the total absorption coefficients (a(λ)). Other
limitations are that the derivation of aph at some specific
wavelengths using one set of equations and at other
wavelengths using different equations. After a thorough
investigation and comparison of our results with those
from the other models (not shown for brevity since it is
already discussed in Shanmugam et al. [28], it was found
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S. P. TIWARI, P. SHANMUGAM 31
Figure 9. MODIS/AQUA data for 18th February 2010 over Arabian Sea, showing the spectral variation of radiance retrieved
from CAAS and SeaDAS in case of Low bloom, Medium bloom, High bloom, and Ve ry high bloom w a ters.
Copyright © 2012 SciRes. ARS
S. P. TIWARI, P. SHANMUGAM
32
that the new model is inherently more flexible for deter-
mination of aph coefficients at any wavelengths in the
visible domain.
6. Conclusion
The new model has significant advantages over other
models, since it relies on the Rrs(670) /Rrs(490) ratio
which is not significantly influenced by materials other
than phytoplankton. Validation of the model with inde-
pendent in-situ data sets gave encouraging results. The
model-predicted aph(λ) values were found to be in good
agreement with in-situ data from coastal/oceanic waters.
The model wavelengths of the SeaWiFS sensor (412 to
683 nm). Though the errors were low (e.g., MRE 8%),
scatter plots showed slight differences between the model
and in-situ aph(λ) values. The difference may arise due to
several reasons; for instance, Rrs(λ) measurements made
with different instruments with different calibration and
correction procedures as well as environmental conditions.
It was demonstrated that the atmospheric correction of
satellite ocean colour data could introduce very high errors
in complex waters. However, such problems could be
eliminated when the water-leaving radiance signals are
estimated with the CAAS algorithm. Thus, the aph(λ)
model may be applied along with the CAAS algorithm,
in order to retrieve more reliable aph(λ) values in opti-
cally complex waters. A MODIS-Aqua example showed
striking features of the distribution pattern of phyto-
plankton absorption coefficients in bloomed waters in the
Arabian Sea. In conclusion, this is the first study to esti-
mate aph(λ) values at all the visible wavelengths. Thus, it
provides new opportunities for improving the phyto-
plankton inversion modelling based on the coefficients as
given in Table 1. Our future effort will include addi-
tional validation and tests based on more in-situ and sat-
ellite data, and refining the model coefficients in order to
provide more accurate phytoplankton absorption coef-
ficients in complex waters.
7. Acknowledgements
This work was supported by INCOIS under the grant
(OEC/1011/102/INCO/PSHA) of the SATCORE pro-
gram. The authors would like to thank the NASA Ocean
Biology Processing Group for making available the
global, high quality bio-optical (NOMAD) data set and
the LAC MODIS-Aqua to this study. The authors would
like to thank J. P. Cannizzaro and C. Hu for providing
the bio-optical datasets of Prof. K. L. Carder.
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