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Characterizing the vertical diffuse attenuation coefficient for
downwelling irradiance in coastal waters: Implications for water
penetration by high resolution satellite data
Deepak R. Mishra
a,
⁎, Sunil Narumalani
a
, Donald Rundquist
a
, Merlin Lawson
b
a
Center for Advanced Land Management Information Technologies, School of Natural Resources,
102E Nebraska Hall, University of Nebraska, Lincoln, NE 68588-0517, USA
b
Department of Geosciences, 306 Bessey Hall, University of Nebraska, Lincoln, NE 68588-0340, USA
Received 1 November 2004; accepted 13 September 2005
Available online 21 November 2005
Abstract
To characterize the water column, the diffuse attenuation coefficient of downwelling irradiance, K
d
(z,λ)(m
−1
) is one of the
most important optical properties of seawater. The purpose of this research was to determine the downwelling diffuse attenuation
coefficient of water around Roatan Island, Honduras. In situ K
d
analysis showed low attenuation coefficient values in green and
blue and increased exponentially after 570 nm. The blue, green and red portion of the spectrum showed a K
d
value of 0.138, 0.158,
and 0.503 m
−1
, respectively. Error analysis revealed a significantly high uncertainty in the red region (600–700 nm) and, as
expected, low estimation uncertainty in blue and green. When compared with IKONOS derived K
d
(490 nm), it was observed that
the differences were negligible, being 0.0084 and 0.0054 m
−1
for station #1 and #2, respectively. Based on the fact that 90% of the
diffused reflected light from a water body comes from a surface layer of water of depth 1 / K
d,
the results showed that a typical
satellite sensor (such as IKONOS) can penetrate up to 8 m in the blue band, 6 m in green, and 2 m in the red region.
© 2005 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights
reserved.
Keywords: Diffuse attenuation coefficient; Downwelling irradiance; Atmospheric correction; Water penetration; IKONOS
1. Introduction
In order to utilize remotely sensed data for monitor-
ing and understanding coastal ecosystems, it is impor-
tant to determine the relationship between water depth
and the reflectance characteristics of various benthic
components. Detailed benthos mapping can be accom-
plished by incorporating accurate bathymetric informa-
tion in the classification process (Mumby et al., 1998).
While remote sensing has been used to map bathymetry,
efforts to employ it have been limited because of the
variable effects of the water column on the reflectance
properties of bottom substrate. Remote sensing scien-
tists have developed strategies to monitor the extent and
vitality of coral reefs, often by assuming the effects of
the water column to be horizontally and vertically ho-
mogeneous (Holden and Ledrew, 2001). Methods for
obtaining bathymetric information from remotely
sensed data described by Lyzenga (1978),Benny and
ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48 –64
www.elsevier.com/locate/isprsjprs
⁎Corresponding author. 102E, Nebraska Hall, University of
Nebraska, Lincoln, Lincoln, NE, 68508, United States. Tel.: +1 402
472 4973; fax: +1 402 472 4608.
E-mail address: dmishra@calmit.unl.edu (D.R. Mishra).
0924-2716/$ - see front matter © 2005 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V.
All rights reserved.
doi:10.1016/j.isprsjprs.2005.09.003
Dawson (1983), and Jupp (1988) have invoked assump-
tions such as the light attenuation is exponential with
depth and that water quality remains consistent within
the image. Stumpf et al. (2003) observed that because of
the difficulties in obtaining sounding data for remote
oceanic regions, information about the bathymetry as-
sociated with globally extensive coral reefs is fragmen-
ted and incomplete. The authors contend that with the
availability of high-resolution imagery (e.g., IKONOS
and QuickBird), new strategies should be developed to
enhance depth estimation techniques by characterizing
the water column.
To characterize the water column, the parameter that
controls the propagation of light through water, i.e., the
diffuse attenuation coefficient, needs to be determined
precisely. This coefficient of downwelling irradiance,
K
d
(z,λ) is of particular interest because it quantifies
the presence of light and the depth of the euphotic
zone. It is defined in terms of the exponential decrease
with depth of the ambient downwelling irradiance E
d
(z,λ), which comprises photons heading in all down-
ward directions (Mobley, 1994):
Kdðz;kÞ¼−1
EdðkÞ
dEd
dz ð1Þ
where,
K
d
(z,λ) diffuse attenuation coefficient (m
−1
);
E
d
(λ) downwelling irradiance (W m
−2
); and
dz the thickness of the medium (m)
K
d
(z,λ) depends on both the composition of the me-
dium and directional structure of the ambient light field;
hence it is classified as an apparent optical property of
the water. Nevertheless, experience has shown that K
d
(z,λ) values are largely determined by the inherent opti-
cal properties of the aquatic medium (e.g., absorption
coefficient and volume scattering function) and are not
altered significantly by changes in the incident radiation
field such as a change in solar elevation (Kirk, 1994).
Considerable research has been done to determine K
d
values for various types of water bodies using in situ as
well as space-borne sensors. Smith and Baker (1978)
classified ocean waters by relating the diffuse attenua-
tion coefficient to plant pigment content, while Jerlov
(1976) used the spectral profile of K
d
to develop a
frequently used classification scheme for oceanic
waters. Similarly, satellite based ocean color sensors
have been used to map optical properties of the ocean
such as K
d
(z,λ) on local and global scales. For example,
data from the Coastal Zone Color Scanner (CZCS) have
been used in numerous studies to describe patterns of
chlorophyll concentration, primary production, and the
diffuse attenuation coefficient (Austin, 1981; Sathyen-
dranath et al., 2000).
The primary purpose of our research was to charac-
terize and map the diffuse attenuation coefficients of
coastal water around Roatan Island, Honduras. This
research used in situ radiometric measurements, as
well as remote sensing, to quantify the diffuse attenua-
tion coefficient for evaluating the feasibility of mapping
shallow water marine habitats. Specifically, the research
included the application of a profile normalization al-
gorithm to in situ underwater downwelling irradiance
measurements for minimizing the effect of changing
sun illumination condition, and characterizing hyper-
spectral diffuse attenuation coefficients. Furthermore,
the study implemented the SeaWiFS algorithm (K
d
(490 nm)) to the normalized water-leaving radiance of
the IKONOS bands (blue and green) to compute the
diffuse attenuation coefficient.
2. Methodology
2.1. Study area and experiment setup
Roatan Island, Honduras lies between 16° 15′to 16°
25′N and 86° 22′to 86° 37′W and is located in the
western portion of the Caribbean Sea approximately 50
km north of the Honduras mainland. The specific study
area for our research is located along the northwestern
coast of Roatan Island in the Sandy Bay Marine Reserve
(Fig. 1). The data were acquired at two locations (see Fig.
1) on 29 March 2004 by a field crew from the Center for
Advanced Land Management Information Technologies,
University of Nebraska–Lincoln. A proximal sensing
platform was used for underwater hyperspectral measure-
ments of the downwelling irradiance. The instrument was
a hand-held wand (appropriately named WANDA) com-
prising of: (a) an upward looking Ocean Optics sensor
(hyperspectral sensor with 2048 bands, 1 nm bandwidth)
with a cosine collector; (b) a downward looking Ocean
Optics sensor; (c) an underwater quantum sensor (PAR
sensor), for broad band downwelling irradiance measure-
ments; (d) a pressure sensor (accuracy of approximately
±5 cm); for depth readings; (e) a camera; and (f) a light
communication system (Fig. 2). An upward looking
Ocean Optics and a quantum sensor were also installed
on the roof of the boat to simultaneously collect down-
welling irradiance with the sensors on the wand. In addi-
tion to the in situ data acquisition, a near-simultaneous
IKONOS satellite image was acquired on the day of the
experiment and was processed to quantify and map the
diffuse attenuation coefficient.
49D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
2.2. In situ data collection and processing
A vertical profile of downwelling irradiance was ac-
quired by a diver lowering WANDA through the water
column at approximately 0.5-m depth intervals. Care
was taken to avoid problems such as diver interference
with the hemispherical field-of-view of the cosine col-
lector (holding the wand at its far end), self-shading by
the instrument (by maintaining the wand position along
the direction of the sun), and maintaining the instrument
attitude with respect to the vertical (using a bubble level
at the end of the wand for the diver). To avoid boat
shadow, readings were taken approximately 20 m away
and on the sunny side of the boat. Two sets of calibration
scans using a Spectralon panel were taken including one
above the surface and the other just below the surface of
the water. Ancillary data such as date and time, geo-
graphic location, direction of the sun relative to the
Fig. 2. Diagram describing the location of the different sensors and experiment setup: a) GPS antenna; b) upward looking Ocean Optics with cosine
collector; c) pyranometer (300 nm–3000 nm); d) quantum sensor; e) light communication device; f) upward looking Ocean Optics with cosine
collector; g) pressure sensor; h) PAR quantum sensor; i) downward looking Ocean Optics; and j) camera.
Fig. 1. Location of Roatan Island, Honduras in Central America (circle inset), and an image-map of the IKONOS scene acquired on 29 March 2004.
Note that the cloud cover at the southern portion of the image was masked out, along with the terrestrial features.
50 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
boat's heading, cloud cover and sky conditions, wind
speed and direction, and the water temperature also were
recorded for each radiometric profile. The light commu-
nication system on WANDA was used when the diver
was stable and ready to acquire the data. After a reading
was acquired, personnel on the boat used the light signal
as an indicator to the diver to proceed to the next depth
level. Consistency of the downwelling irradiance read-
ings between the upward looking Ocean Optics sensors
(on WANDA and the boat) were checked several times
before deploying WANDA. Sky irradiance readings
were taken by Ocean Optics mounted on the boat, in
between the underwater measurements to minimize the
effect of sea-state, wave action, and changing illumina-
tion conditions.
2.2.1. Normalization of downwelling irradiance
Changes in sun illumination condition may cause
variations in incident surface irradiance, E
s
(z,λ) mea-
sured at a given time t(z). In present usage, E
s
(t(z
m
), λ)
refers to the incident spectral irradiance measured from
the roof of the boat at time t(z
m
) and E
d
(z
m
,λ) refers to
the downwelling irradiance at water depth zmeasured
by WANDA. Mueller (2000) proposed that all scans be
normalized to a specific scan (e.g., first scan) in order to
quantify the variation in the obtained downwelling irra-
diance spectra because of changes in sun illumination
by cloud cover. Our experiment consisted of 24 scans
and the normalization factor was obtained as:
Normalization factor ðzm;kÞ¼Esðtðz1Þ;kÞ
EsðtðzmÞ;kÞð2Þ
where,
E
s
(t(z
1
), λ) = the downwelling irradiance measured at
time t(z
1
) on the boat at the first scan.
To examine how the sky condition changed during
the 24 scans with reference to the first scan, the nor-
malization factors for selected wavelengths of 1-nm
bandwidth (450, 550, and 650 nm—being the mid-
points of the blue, green, and red wavelengths) were
plotted against the number of scans (Fig. 3a). The graph
showed that sky conditions changed considerably for all
scans when compared to Scan 1. Scans showing a
normalization factor of greater than 1 indicate shadows
(or lower irradiance) while those less than 1 are indic-
ative of brighter conditions. In general, Scans 8, 18, 21,
and 23 showed similar sky condition to Scan 1, while
Scans 1–7 and 9–17 were acquired under lower illumi-
nation conditions (see Fig. 3a). Variations in the nor-
malization factor between wavelengths are due to the
differences in the sensitivity of each wavelength to
incoming radiant energy.
To further establish the changing sky conditions, the
normalization factor was obtained from another broad-
band quantum sensor installed on the roof of the boat
and compared with the Ocean Optics data (integrated
over 400–700 nm) (Fig. 3b). A high correlation
(R
2
= 0.99) was observed between the two sensors,
thus concluding that sun illumination conditions
changed during the experiment.
Assuming that transmission of surface irradiance (E
s
(t(z
m
), λ)) through the water column does not vary with
time, a normalization of the downwelling irradiance can
be derived as:
Ed
Vðzm;kÞ¼Edðzm;kÞEsðtðz1Þ;kÞ
EsðtðzmÞ;kÞð3Þ
where,
E
d
′(z
m
,λ) the normalized downwelling irradiance at
that depth (z
m
)
E
d
(z
m
,λ) the original downwelling irradiance at depth
(z
m
) recorded by Ocean Optics during profile
measurements.
Pre- and post-normalization spectra were compared
and it was observed that the variance between the scans
had decreased along the entire spectrum. This indicated
that extraneous noise (e.g., change in sun illumination)
had been effectively eliminated.
2.2.2. Derivation of K
d
(z, λ)
The decrease in the intensity of light as it travels
through the water column is called light attenuation,
which is caused by the combined absorption and scat-
tering properties of all matter in the water column,
including the water itself. Beer's law states that intensity
of light decreases exponentially as a function of depth
in the water column and is described mathematically
as:
E¼E0eð−KzÞð4Þ
where,
Eirradiance at a given depth
E
0
irradiance at the surface
Kattenuation coefficient
zdepth.
In our experiment, downwelling irradiance measure-
ments were taken at several depths and normalized for
changing sun illumination condition, so Beer's law can
be modified to:
Ed
Vðzm;kÞ¼Ed
Vðz1;kÞe
−Rzm
z1
KdðzV;kÞdz V
ð5Þ
51D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
where,
E
d
′(z
m
,λ) normalized downwelling irradiance at depth
z
m
E
d
′(z
1
,λ) the normalized downwelling irradiance at
depth z
1
dz
′depth interval.
To simplify Eq. (5), the natural logarithm is derived
as follows:
−Zzm
z1
KdðzVÞdz
V¼ln½Ed
Vðzm;kÞ−ln½Ed
Vðz1;kÞ ð6Þ
Furthermore, assuming K
d
(z′) being constant for
all dz′(the assumption was made after analyzing the
K
d
values for different dz; the results showed very
little difference in the K
d
value), Eq. (6) can be
modified as:
−KdðzÞðzm−z1Þ¼ln Ed
Vðzm;kÞ
Ed
Vðz1;kÞ
ð7Þ
Eq. (7) corresponds to the equation of a straight line
passing through the origin (y=mx). If ln Ed
Vðzm;kÞ
Ed
Vðz1;kÞ
hi
is
plotted versus (z
m
−z
1
), the local slope will provide us
with the diffused attenuation coefficient (−K
d
(z), λ).
2.2.3. Erroneous scan elimination and error estimation
Wave focusing and air/water interface effects may
induce error in the irradiance measurements recorded
just below the surface of water. The erroneous scans can
Fig. 3. a) Distribution of normalization factor at each scan, showing the dynamic nature of sky condition; and b) comparison of the integrated
normalization factor at each scan, between the ocean optics radiometer and quantum sensor.
52 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
be identified by analyzing the plot of ln[E
d
(z
m
)/E
d
(z
1
)]
versus (z
m
−z
1
), for any wavelength. In Fig. 4, using 550
nm as an example, it was observed that six scans (circled)
within 2 m from the water surface were clumped together
and exhibited a different trend than the rest of the scans.
Three of these scans showed the attenuation values being
greater than zero, which implies that at those depths there
was more light available than at the surface. Since such a
scenario is very unlikely, these six scans were removed
from further analysis. After removing these six scans, the
plot of ln[E
d
(z
m
)/E
d
(z
1
)] versus (z
m
−z
1
) was analyzed for
three wavelengths (bandwidth= 1 nm) including 450,
550, and 650 nm. Results showed K
d
values of 0.15,
0.14, and 0.66 m
−1
for the three wavelengths, with a
standard estimation error of 0.006, 0.003, and 0.108
m
−1
,respectively(Fig. 5). The hyperspectral (301 bands
between 400 and 700 nm, 1-nm bandwidth) diffuse at-
tenuation coefficient was calculated using Eq. (7) and an
error estimation was performed using the following
algorithm:
Std:Errorslope ¼X
N
1
ðYi−ŶiÞ2
ðN−2ÞX
N
1
ðXi−X
iÞ2
ð8Þ
where,
Y
i
calculated value of ln[(E
d
(z
m
)/E
d
(z
1
)] for each
wavelength
Fig. 4. Points used (square) and not used (inside circle) in the analysis of K
d
in the plot of ln[E
d
′(z
m
)/E
d
′(z
1
)] versus (z
m
−z
1
) at 550 nm.
Fig. 5. Distribution of points used in the analysis of K
d
at 450 nm, 550 nm, and 650 nm.
53D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
Ŷ
i
predicted value of ln[(E
d
(z
m
)/E
d
(z
1
)] for each
wavelength
X
i
depth interval (dz) (m) for each scan
X
¯
i
mean depth interval (m)
Nnumber of scans, which is 18 in our case.
The final step of our methodology was to apply
Gordon's normalization procedure to the calculated K
d
values to remove the effects of the sea state and diffuse
sky irradiance (Gordon, 1989).
2.2.4. Gordon's normalization
Sky irradiance readings taken during the experiment
by shading the surface ocean optics were used in the
Gordon's normalization process. The normalization
equation is given as
KdðnormalizedÞ¼KdðmeasuredÞ
D0
ð9Þ
where,
D0¼f
coshsw
þ1:197ð1−fÞð10Þ
D
0
is a distribution function that reduces K
d
values
and removes the effect of sea state and sky irradiance;
θ
sw
is the nadir angle of a transmitted solar beam and is
related to solar zenith angle (θ
s
) as:
hsw ¼sin−1sinhs
1:34
ð11Þ
Where, 1.34 is the index of refraction of water. fis
the fraction of direct sunlight in the incident irradiance
that is transmitted through the surface into the water and
is computed as:
f¼EdðsunÞ
EdðtotalÞ¼EdðsunÞ
EdðsunÞþEdðskyÞð12Þ
fvalues are indicative of how much direct sunlight was
available for that specific scan, and in the absence of
diffuse sky irradiance the values approach 1. Converse-
ly, if the sky is overcast or hazy the fvalues are less than
1. Using Scan 1 as the baseline, a comparative evalua-
tion of fvalues was made for those scans with the
maximum variation in sun illumination. From Fig. 3a
and b, it was observed that Scans 14 and 19 had the
maximum deviation from Scan 1. The fvalues revealed
that Scan 19 had more direct sunlight when compared to
Scans 1 (baseline) and 14, which had the highest diffuse
sky irradiance (Fig. 6). Thus, Eq. (9) normalizes these
variations of sky irradiance and makes K
d
an inherent
optical property of the seawater.
2.2.5. Comparative evaluations
A comparison of the derived K
d
values was per-
formed against the K
d
values of: (a) pure seawater by
Smith and Baker (1981); and (b) the calculated beam
attenuation coefficient cfrom the absorption coefficient
of pure water given by Buiteveld et al. (1994). The
beam attenuation coefficient was expressed as
c¼aþbð13Þ
where,
aabsorption coefficient
bscattering coefficient.
Fig. 6. The availability of direct sunlight compared between the highly variable scans.
54 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
The scattering coefficient at each wavelength, sug-
gested by Morel (1974), was calculated as:
bðkÞ¼0:0011 k
500
−4:32
ð14Þ
2.3. Satellite image acquisition and processing
IKONOS panchromatic and multispectral images
were collected for the Roatan study site on 29 March
2004, on the same day as the ground experiment. Pri-
mary radiometric corrections by Space Imaging, Inc.,
Colorado, USA, were designed to remove any spatial
variations in digital output or artifacts that may occur in
the image data. Geometric corrections (+ 1 pixel; nearest
neighbor) were performed to remove any optical or
positional distortions in the imagery. Thirty ground
control points and a polynomial geometric model were
used in the image-to-image geometric rectification pro-
cess. The brightness values (BVs) for each band were
converted to top of the atmosphere (TOA) radiance by
applying calibration coefficients referenced to well-
characterized spectro-radiometric targets.
2.3.1. Land and cloud masking
When extracting aquatic information, it is useful to
eliminate all upland and terrestrial features (Jensen et
al., 1991); thus all upland features, as well as boats,
piers, and clouds, were masked out of the image. The
“land-mask”restricts the spectral range of BVs to aquat-
ic features and allows for detailed feature discrimina-
tion. Radiance values of the NIR band were used to
prepare the binary mask which was subsequently ap-
plied to all the bands. Although 13% cloud cover in the
image was successfully masked out, cloud shadows on
the water bodies still remained and could not be re-
moved because their radiance values were similar to
the other water areas. Fortunately, the area where the
ground experiment was performed did not have any
cloud cover or shadows, and the image was subset to
that region for further analysis.
2.3.2. First order atmospheric correction
In the case of oceanic remote sensing, the total signal
received at the satellite altitude is dominated by radi-
ance contributed through atmospheric scattering pro-
cesses and only 8–10% of the signal corresponds to
the oceanic reflectance (Kirk, 1994). Therefore, it is
advisable to correct for atmospheric effects to retrieve
any quantitative information for surface waters from the
image. The radiance received by a sensor at the TOA in
a spectral band centered at a wavelength λ
i
,L
t
(λ
i
), can
be divided into the following components (Gordon et
al., 1983):
LtðkiÞ¼LrðkiÞþLaðkiÞþTðkiÞLgðkiÞ
þtðkiÞLwðkiÞð15Þ
where,
L
r
(λ
i
) and L
a
(λ
i
) radiances generated along the optical
path in the atmosphere by Rayleigh and aero-
sol scattering, respectively;
Tdirect atmospheric transmittance;
L
g
(λ
i
) contribution arising from the specular reflec-
tion of direct sunlight from the sea surface or
the sun glint component;
tdiffuse atmospheric transmittance of the atmo-
sphere; and
L
w
(λ
i
) desired water leaving radiance.
Note that, for an atmosphere with high visibility
(≈40 km), we ignore any Rayleigh-aerosol multiple
scattering and use a quasi-single-scattering approxima-
tion. According to Gordon and Voss (1999), for areas
around the sun glint pattern, T(λ
i
)L
g
(λ
i
) is so large that
the imagery is virtually useless and must be discarded.
Since the IKONOS image had negligible sun glint
effects, T(λ
i
)L
g
(λ
i
) may be ignored, leaving the largest
and most difficult terms to estimate—i.e., the path
radiances due to Rayleigh and aerosol scattering. Con-
sequently, Eq. (15) can be written as:
LtðkiÞ¼LrðkiÞþLaðkiÞþtðkiÞLwðkiÞð16Þ
2.3.2.1. Computation of Rayleigh path radiance (L
r
(λ
i
)). Rayleigh atmospheric scattering primarily af-
fects the direction of short wave radiation, resulting in
haze in the blue and green bands. For Landsat MSS data,
the Rayleigh scattering is four times greater in the green
band of the electromagnetic spectrum than in the near
infrared band (Jensen, 1986). Rayleigh path radiance
can be computed using Gordon and Clark (1981) as:
LrðkiÞ¼F0
VðkÞx0srPr
4pcosh0
ð17Þ
where,
F
0
′(λ) instantaneous extraterrestrial solar irradiance.
F
0
′(λ), which is reduced by two trips through
the ozone layer, is computed by:
F0
VðkÞ¼F0ðkÞe−sOzð1=coshvþ1=cosh0Þð18Þ
55D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
F
0
(λ) values are taken from Nickel and Labs
(1984);
ω
0
single scattering albedo equal to 1;
τ
r
Rayleigh optical thickness;
P
r
Rayleigh scattering phase function;
τ
Oz
Ozone optical thickness;
θ
v
satellite viewing zenith angle; and
θ
0
solar zenith angle
The value of Rayleigh optical thickness (τ
r
) at any
atmospheric pressure Pis given by Hansen and Travis
(1974):
sr¼P
P0
½0:008569k−4ð1þ0:0113k−2þ0:00013k−4Þ
ð19Þ
where,
λwavelength in micrometers; and
P
0
standard atmospheric pressure of 1013.25 mbar.
The Rayleigh scattering phase function is given by
Doerffer (1992):
PrðhFÞ¼3
4ð1þcos2hFÞð20Þ
where,
θ
±
forward/backward scattering angle and is relat-
ed to the sensor viewing and solar illumination
directions through:
coshF¼Fcosh0coshv−sinh0sinhvcosð/v
−/0Þð21Þ
where,
θ
0
solar zenith angle;
ϕ
0
solar azimuth angle;
θ
v
satellite viewing zenith angle; and
ϕ
v
satellite viewing azimuth angle.
2.3.2.2. Computation of aerosol path radiance (L
a
(λ
i
)). To compute aerosol scattering for the scene,
we assumed that for the NIR band 4 (805 nm) the
water leaving radiance (L
w
(λ
i
)) over the clear-water
pixels would be close to zero because of the absorp-
tion by water. Hence, the measured TOA radiance (L
t
(λ
i
)) in the NIR is the sum of Rayleigh (L
r
(λ
i
)) and
aerosol path radiance (L
a
(λ
i
)). By subtracting Rayleigh
path radiance from the TOA radiance in clear water
pixels of the NIR band, one can deduce aerosol path
radiance for those pixels. We computed the contribu-
tion of aerosol scattering for a window of 50 × 50
clear water pixels as:
L0
aðk4Þ¼L0
tðk4Þ−L0
rðk4Þð22Þ
where,
L
a
0
(λ
4
) contribution of aerosol scattering over the clear
water pixels at band 4;
L
t
0
(λ
4
) total radiance observed over the clear water
pixel at band 4; and
L
r
0
(λ
4
) contribution of Rayleigh scattering over the
clear water pixels at band 4.
Aerosol path radiance at any wavelength, L
a
0
(λ
i
), can
be calculated from L
a
0
(λ
4
) and is given as:
LaðkiÞ¼Sðki;k4ÞL0
aðk4Þð23Þ
where,
Sa ratio, which is related to the optical proper-
ties of the aerosol through:
Sðki;k4Þ¼eðki;k4ÞF0
VðkiÞ
F0
Vðk4Þð24Þ
Gordon and Wang (1994) proposed an exponential
relationship for the spectral behavior of aerosol optical
depth which has been used for the SeaWiFs atmospheric
correction algorithm. The algorithm uses an Angstrom
exponent (ɛ) based on an exponential relation using
spectral data at 765 and 865 nm for each pixel. The
aerosol optical thickness is extrapolated to the visible
channels using this relationship. Because the IKONOS
sensor does not have two bands in the NIR to calculate
the Angstrom exponent, ɛ(λ
i
,λ
4
) was set to unity, which
is characteristic of maritime aerosols at high relative
humidity (Gordon and Voss, 1999). We also assumed
that the aerosols are homogenously distributed over the
entire area of interest, so that L
a
0
(λ
4
) is computed over
the clear water (50 × 50 window) and assumed to be
Table 1
Comparison of average K
d
values and associated error in blue, green,
and red portion of electromagnetic spectrum at both ground stations
Wavelength (nm) Average
K
d
(m
−1
)
station #1
Average
error (m
−1
)
station #1
Average
K
d
(m
−1
)
station #2
Average
error (m
−1
)
station #2
Blue (400–500 nm) 0.138 0.004 0.112 0.007
Green
(500–600 nm)
0.158 0.006 0.135 0.009
Red (600–700 nm) 0.503 0.063 0.48 0.129
56 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
constant over the entire IKONOS scene. Hence, the
aerosol path radiance for the three visible bands was
computed using Eq. (23).
2.3.2.3. Computation of diffuse transmittance (t
(λ
i
)). Diffuse transmittance (t(λ
i
)) is defined as the
water leaving radiance in a particular viewing direction
(θ
0
,θ
v
) transmitted to the top of the atmosphere and is
given by
tðkiÞ¼exp −srðkÞ
2þsOzðkÞ
1
cosh0
þ1
coshv
ð25Þ
where,
τ
r
(λ) Rayleigh optical thickness; and
τ
Oz
(λ) ozone optical depth. Ozone optical depth for a
concentration of DU (Dobson units or milliat-
mosphere centimeters) is given by:
sOzðkÞ¼kOz ðkÞDU
1000 ð26Þ
where,
k
Oz
(λ) ozone absorption coefficient taken from Leck-
ner (1978).
The desirable water-leaving radiance (L
w
(λ
i
)) at a spe-
cific wavelength was computed by rewriting Eq. (16) as:
LwðkiÞ¼LtðkiÞ−LrðkiÞ−LaðkiÞ
tðkiÞð27Þ
Fig. 7. Hyperspectral diffuse attenuation coefficient spectra for downwelling irradiance in the visible region: a) for Station #1, and b) for Station #2.
Dotted lines are the estimation error observed at each wavelength.
57D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
2.3.3. Diffuse attenuation coefficient (deriving the K
d
for IKONOS)
Although Austin and Petzold (1981) derived a K
Lu
(490) algorithm for the NIMBUS-7 Coastal Zone
Color Scanner (CZCS) for the upwelling radiance at-
tenuation coefficient (K
Lu
), both the SeaWiFs and
MODIS algorithm replace K
Lu
with the attenuation
coefficient for downwelling irradiance, K
d
. The algo-
rithm to estimate MODIS K
d
(490) uses the MODIS
band ratio of normalized water-leaving radiances (nL
w
(λ
i
)) at 488 and 547 nm. The normalized water-leaving
radiance is approximately the radiance that would exit
the ocean in the absence of the atmosphere with the
sun at the zenith, and has been defined by Gordon and
Clark (1981) as:
LwðkiÞ¼½nLwðkiÞcosh0
exp −srðkiÞ
2þsOzðkiÞ
1
cosh0
ð28Þ
Following Eq. (28), the MODIS K
d
(also used to
compute the SeaWiFs K
d
) is defined as follows:
Kdð490Þ¼0:016 þ0:15645 nLwð488Þ
nLwð547Þ
−1:5401
ð29Þ
where,
0.016 the pure water diffuse attenuation coefficient at
490 nm (based on Pope and Fry (1997), and
modified by Mueller, 2000); and
0.15645 and −1.5401 coefficients determined by re-
gression analysis (Mueller, 2000).
The change in coefficients due to substitution of
spectral bands (from MODIS 488 nm and 547 nm to
IKONOS' 480 nm and 551 nm) has not been addressed,
but is expected to be small (Mueller, 2000).
3. Results and discussion
3.1. In situ
Our results discuss the characteristics of derived K
d
values (i.e., prior to Gordon's normalization) and com-
pares them to the broadband quantum sensor, followed
by an analysis of the K
d
after normalization. In general,
there was increasing light attenuation from blue through
red at both experiment stations (Table 1;Fig. 7a and b).
Part of the green region (500–550 nm) showed lower
diffuse attenuation coefficient values than the blue re-
gion because of absorption by chlorophyll in blue by
phytoplankton cells.
Attenuation of light in water increases with wave-
length, and this is evident in our experiment, where a
sharp increase is detected from 560 nm onward,
becoming exponential in the red spectrum (see Fig.
7a and b). In Roatan, where the water is clear,
absorption of the red light by water itself is higher
because of the lack of scattering by suspended parti-
cles. As the water depth increases, the light becomes
more diffuse and red absorption increases. This can
be visualized from Fig. 8, which shows the photon
availability ratio in blue-green (400–600 nm) and red
Fig. 8. Photon availability at blue-green and red spectra compared to the total photosynthetic range as a function of depth.
58 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
(600–700 nm) when compared to the whole photo-
synthetic range (400–700 nm), thus indicating that as
water depth increases there is more blue-green light
available than red light. In fact, a substantial drop-off
in red light that is detected even after 2 m depth
implies that fewer photons are available in the red,
which in turn decreases the signal-to-noise ratio and
increases the estimation error of K
d
. Therefore, error
analysis (dotted lines in Fig. 7a and b) shows a
greater deviation in the red region (600–700 nm)
when compared to blue and green portions of the
spectrum.
An underwater broadband (400–700 nm) quantum
sensor also was used to acquire the downwelling irradi-
ance simultaneously with the hyperspectral Ocean Op-
tics. Broadband downwelling irradiance decreased with
depth and revealed a nonlinear relationship of logarith-
mic nature (Fig. 9a). K
d
analysis for the broadband
underwater quantum sensor showed a value of 0.184
m
−1
with an error of +0.008 m
−1
for Station #1 (Fig.
9b). When compared with the integrated hyperspectral
K
d
obtained from the Ocean Optics, a difference of
0.064 m
−1
was observed. Similar results were obtained
for Station #2 where the broadband quantum sensor
showed a K
d
of 0.174 m
−1
and the difference between
the Ocean Optics was 0.071 m
−1
. This disparity is due
to the difference in the response functions of the two
instruments and the high error (see Table 1) induced
in the Ocean Optics hyperspectral K
d
values beyond
600 nm.
Fig. 9. Distribution of points used in the analysis of K
d
for the underwater quantum sensor: (a) depth profile of quantum irradiance; and (b)
attenuation coefficient for broadband quantum sensor in the plot of ln[E
d
(z
m
)/E
d
(z
1
)] versus (z
m
−z
1
).
59D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
Gordon's normalization was applied to the calculat-
ed K
d
values and produced similar results with rela-
tively less attenuation in all wavelengths, with the
difference between the pre-and post-normalized K
d
values being higher in the red than in the blue-green
(Fig. 10). The small difference observed between pre-
and post-normalized K
d
is in accordance with Kirk
(1994), who suggested that K
d
values are largely de-
termined by composition of the water and not altered
much by the changes in the incident radiation field.
The comparison of calculated K
d
at both stations with
K
d
of pure sea water, and c(Eq. (13)) of pure water,
showed that cwas lower than both K
d
values in all
spectral regions with the difference increasing towards
the red spectrum because of the high attenuation of
diffused light compare to collimated light (Fig. 11).
The K
d
for the two stations showed higher values in
all wavelength regions when compared to the pure
sea water. This can be attributed to the cumulative
effect of absorption by phytoplankton cells and scat-
tering by suspended sediment present in Roatan
water.
3.2. Satellite image analysis
Radiance values of water over different bottom
types were analyzed before and after the atmos-
pheric correction. Since TOA radiance values are
Fig. 10. Hyperspectral diffuse attenuation spectra before and after Gordon's normalization.
Fig. 11. Comparison between derived attenuation coefficients of different water types from earlier published results.
60 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
dominated by Rayleigh and aerosol path radiance, it
becomes difficult to infer the spectral properties of
water over different benthic substrate. To fully un-
derstand this concept, known pixels depicting water
over five locations including shallow water, sea-
grass, deep water, submerged sand, and coral reef
areas were selected (Fig. 12). After the atmospheric
correction was implemented, the corrected profiles
show the spectral variability in greater detail. For
example, NIR water leaving radiance becomes al-
most 0 in all the cases because of high NIR ab-
sorption by water. Similarly, seagrass areas and deep
water showed low radiance values. Water-leaving
radiance always contains a fraction of upwelling
radiance of the underlying benthic habitat. When
comparing water-leaving radiance over shallow
areas, submerged sand or coral reefs to seagrass
areas, it can be observed that the seagrass substrate,
being darker, has low upwelling radiance. Converse-
ly, submerged sand (being the brightest substrate)
had the maximum radiance values. In general, the
green band was found to have the highest water
leaving radiance amongst all IKONOS bands. Spe-
cific absorption features of different benthic bottom
types are not identifiable because of the water col-
umn and the broadband nature of the IKONOS
sensor.
Jerlov (1976) used the value of K
d
to develop a
classification scheme for ocean waters. Accordingly,
open ocean water types were classed as I, IA, IB and
III, while coastal waters were labeled 1 through 9.
The K
d
image generated in this study could be
grouped into three major categories ranging from
coastal areas to deep ocean including 0.03–0.09
m
−1
, 0.09–0.15 m
−1
, and 0.15–0.40 m
−1
(Fig. 13).
Based on the classification by Jerlov (1976), the
waters off Roatan can be classified from IKONOS
data as oceanic water type IA and II (K
d
range
0.03–0.09 m
−1
) and type 1 (K
d
range N0.14 m
−1
)at
490 nm. The general, K
d
pattern shows a decline as
one transits from the coastal area to the deep ocean.
Near the coast, wave action or human influence (e.g.,
effluence, boating, and fishing) adds suspended par-
ticulate matter leading to increased attenuation. Con-
versely, in the deeper reaches of the water, the
disturbances are either minimal or non-existent and
the water is free and clear of any suspended material
leading to lower K
d
values. On the east side of the
study area, intermediate and high K
d
values can be
found in a strip paralleling the coastline, while the
lowest values are observed in the deep water. How-
ever, the west side of the island shows a greater
variation in the K
d
values because of the different
depth structure, and benthic substrate distribution.
Fig. 12. TOA and water-leaving radiances (W m
−2
sr
−1
μm
−1
) derived from IKONOS data over different bottom types.
61D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
Here, the northern part (near Half Moon Bay) is
comprised of clear deep water, leading to the lowest
observed K
d
values. As we transit westward, the wave
action around the coral reefs produces turbidity result-
ing in an increased K
d
. In the southwest portion of
the study area (known as West End), a “typical”K
d
pattern is observed, with decreasing attenuation from
coast/upland interface toward the open ocean.
Further analysis was performed to compare the K
d
(490) values derived from the two ground stations
with the satellite derived K
d
values (Table 2). The
differences were negligible, being 0.0084 m
−1
for
Station #1 and 0.0054m
−1
for Station #2, respectively.
To examine the depth of water column that a satellite
sensor can detect without taking into account the
atmospheric effect, the function (1 / K
d
) was plotted
versus wavelength for the study area (Smith and
Baker, 1978). Based on the fact that 90% of the
diffused reflected light from a water body comes
from a surface layer of water of depth 1 / K
d
, the
results showed that a typical satellite sensor (such as
IKONOS) can penetrate up to 8 m in the blue band, 6
m in green, and 2 m in red region (Fig. 14). It
indicates that in areas where water itself is the main
absorber, blue and green light can penetrate deeply,
while red light, is rapidly attenuated. Our results
indicate that a portion of the green band (500–550
Fig. 13. Vertical diffuse attenuation coefficient K
d
(490 nm) derived from IKONOS multispectral data.
Table 2
Comparison of K
d
(490) values derived from IKONOS and ground
experiment
Station
#
Latitude
(°N)
Longitude
(°W)
K
d
(490)
(IKONOS)
(m
−1
)
Average K
d
(490)
(field experiment)
(m
−1
)
1 16°16.41′86°36.14′0.1152 0.1236
2 16°17.01′86°36.15′0.1036 0.0982
62 D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
nm) would be the most suitable for remote sensing of
benthic habitat around Roatan Island.
4. Conclusion
The value of K
d
is dependent (although weakly) on
change in solar zenith angle as it is an apparent optical
property of water. In the case of one of our in situ
experiments, the range of solar zenith angle starting
from the Scan 1 to the last Scan (#24) was 3.6° (from
43.1° to 46.7°), indicating that the experiment was
performed over a short time period. When K
d
is deter-
mined by profiling methods, a trade-off exists between
rapid profiling to maintain a relatively constant solar
zenith angle during measurements, and a longer sam-
pling interval at each depth to minimize fluctuation
caused by waves and wave focusing effects. A profiling
method cannot be used to cover a wide and continuous
zenith angle range. Alternatively, radiometers deployed
on a mooring at discrete depths provide a means for
monitoring long-term ocean optical properties with high
temporal resolution.
The water around Roatan Island is classified as Case
I based on Morel and Prieur (1977), which implies that
the concentration of phytoplankton is high compared to
non-biogenic particles. Case I waters can range from
very clear (oligotrophic) to very turbid (eutrophic),
depending on the phytoplankton concentration These
diverse microscopic plants contain chlorophyll and re-
lated pigments that strongly absorb light in blue and red,
and because they are much larger than the wavelength
of visible light, they can strongly influence the total
scattering properties of sea water (Mobley, 1994). Con-
sequently, they increase the values of K
d
by their spe-
cific absorption and scattering properties. Chlorophyll
concentration in Roatan water varies between 0.2–0.4
mg/m
3
(based on in situ measurements) and that is the
reason why K
d
values in water around the Roatan Island
are found higher than that of pure sea water given by
Smith and Baker (1981), and why blue light is attenu-
ated more strongly than green light, but not as strongly
as red light (see Fig. 12). The MODIS K
d
(490) algo-
rithm used in this case worked well for deep water areas
such as in Station #1 and #2. However, it showed
anomalous results near the beach areas, where water
depth is less than 2 m with sand bottom. This result
can be attributed to the fact that the MODIS K
d
(490)
algorithm was developed for Open Ocean and works
well in areas where ocean bottom is not visible in the
satellite imagery. Another fact which cannot be ignored
in our case is the MODIS K
d
(490) algorithm uses
narrow bands (i.e., 20 nm in MODIS), whereas we
used IKONOS bands which are fairly wide (71.3,
88.6, 65.8, 95.4 nm for blue, green, red, and NIR,
respectively).
Despite the many variables (e.g., boat shadow, sea
state, cloud cover) affecting the K
d
values and a
hostile environment for data collection, knowledge
of this parameter is valuable, not only because it
provides information about how much light is avail-
able for photosynthesis, but also because it offers an
insight about the water depth to which a satellite
sensor can be used for benthic habitat mapping. Fur-
ther research will make use of the derived K
d
values
for removing the water column effects from a satellite
image and for aiding benthic habitat mapping.
Fig. 14. Depth of penetration of light at different wavelengths calculated from 1 / K
d
at both stations.
63D.R. Mishra et al. / ISPRS Journal of Photogrammetry & Remote Sensing 60 (2005) 48–64
Acknowledgements
The authors thank the 2004 Roatan field crew of the
Center for Advanced Land Management Information
Technologies (CALMIT), University of Nebraska–Lin-
coln (UNL), for their data collection efforts. Thanks are
due also to Jennifer Keck of the Roatan Institute for
Marine Sciences (RIMS), Roatan, Honduras, as well as
the staff members of Anthony's Key Resort in Roatan
who assisted in the research conducted at that location.
Special thanks to Giorgio Dall'Olmo, and Dr. Anatoly
Gitelson (CALMIT) for their valuable input.
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