Correction methods for low-altitude
remote sensing of ocean color
Gordana Lazin
Submitted in partial fulfillment of the requirements
for the degree of Master of Science
Dalhousie University
Halifax, Nova Scotia,
November, 1998
O Copyright by Gordana Lazin, 1998
National Library
Bibliothèque nationale
du Canada
Acquisitions and
Bibliographie Services
Acquisitions et
services bibliographiques
395 Weilinglon Street
Ottawa ON K1A 0)54
395. nie Wellington
OiîawaON K 1 A W
canada
Canada
The author has granted a nonexclusive licence allowing the
National Library of Canada to
reproduce, loan, distribute or seil
copies of this thesis in microforrn,
paper or electronic formats.
L'auteur a accordé une licence non
exclusive permettant à la
Biblioîhèque nationale du Canada de
reproduire, prêter, distribuer ou
vendre des copies de cette thèse sous
la forme de microfiche/nlm, de
reproduction sur papier ou sur format
électronique.
The author retains ownership of the
copyright in this thesis. Neither the
thesis nor substantial extracts fiom it
may be printed or othenvise
reproduced without the author's
permission.
L'auteur conserve la propriété du
droit d'auteur qui protège cette thèse.
Ni la thèse ni des extraits substantiels
de celle-ci ne doivent être imprimés
ou autrement reproduits sans son
autorisation.
Table of Contents ............................................................................................................. iv
List of Figures................................................................................................................... vi
List of tables ...................................................................................................................... i x
Abstract ............................................................................................................................
x
List of symbds nad abbreviations ................................................................................ xi
...
.............................................................................................. xi11
Acknowledgments.....
.
.
.
Introduction ...................................................................................................................
1
Chapter 1 Background.............................................................................................
1 -1 Ocean color ................................................................................................................
4
4
1 -2 Water-leaving radiance ..............................................................................................5
1.3 Remote measurements of ocean color .................................... .-.
............................ 7
1 -4 Platforms for remote sensing ..................................................................................10
Chapter 2 Shipbrne remote sensing .............................................................
13
2.1 Measurernent of ocean color above the surface ....................................................... 13
2.2 Surface reflection ..................................................................................................... 15
2.2.1 Reflection of sunlight from the surface ............................................................ 16
2.2.2 Reflection of sky light from the surface ............................................................
17
2.3 Review of existing methods for surface giint correction ........................................ 20
2.4 Proposed method for surface glint correction .......................................................... 23
2.5 Data and Methods ....................................................................................................
26
2.5.1 Data .................................................................................................................... 26
2.5.2 Water-leaving radiance ...................................................................................... 29
2.5.3 Remote sensing reflectance and chlorophyll algorithm ..................................... 30
2.5.4 Statistical tests and errors .................................................................................. 31
2.6 Results and discussion ............................................................................................. 32
2.6.1 Results ............................................................................................................... 32
2.6.2 Discussion ................................................................................................
4
2.7 Conclusion ...............................................................................................................
5
53
Chapter 3 Airborne remoh s e n h g .................................................................. 54
3.1 Measurements of ocean color from aircraft ............................................................. 54
3.2 Atmosphenc constituents and processes .................................................................. 55
3.2.1 Atmospheric attenuation.................................................................................... 55
3.2.2 Rayieigh scattering ...........................................................................................5 6
3.2.3 Aerosol scattering .........................................................
.
.
.
............................. 57
3.3 Existing methods for atrnospheric correction .......................................................... 58
3 -4 Data and Methods .................................................................................................... 60
3.4.1 Data............................... .
.
.
.
.......................................................................... 60
3.4.2 Computation of water-leaving radiance............................................................. 61
3.4.3 Atmospheric and surface glint correction..................................................... 63
3.4.4 Chlorophy11 idgorithm .......................................................................................
67
3.5 Results and discussion .............................................................................................
69
3.5.1 Cornparison of radiances ...................................................................................69
3.5.2 Sunny conditions ............................................................................................... 70
3.6.3 Overcast conditions ..........................................................................................
86
3.6 Conclusion ............................................................................................................... 88
Chapter 4 Summary................................................................................................
90
Appendix A Cox and Munk mode1 for sun-gliat........................................................
92
References ........................................................................................................................
94
List of Figures
Figure 1.3-1
The different origins of light received by a remote sensor pointed to the
ocean surface. .............................................................................................. 8
Figure 1.3-2 Definition of the angles involved in rernote sensing. .................................. 9
Figure 2.1 - 1
Spectral distribution of direct sun and difise sky irradiance. .................. 14
Figure 2.2- 1
Reflection from a rough sea surface.. ........................................................ 18
Figure 2.6-1
Before correction: Comparison of total radiance measured above the
surface to
the
water-leaving
radiance
estimated
from
in-water
measurements ........................................................................................... 3 7
Figure 2.6-2
Before correction: Comparison of remote sensing reflectance ratios
calculated from total above-surface radiance to the ratios estimated from
in-water measurements.............................................................................. 38
Figure 2.6-3
Relationship between sky-glint and difise downwelling irradiance........ 39
Figure 2.6-4
After correction: Comparison of water-leaving radiance retneved by
correction method, and L,estimated from in-water measurements.. .......- 4 0
Figure 2.6-5
The deviations (bises) of water-leaving radiances derived by correction
method from the ones estimated from in-water rneasurements vs.
wavelength.. .................................... .. ..................................................... - 41
Figure 2.6-6
Relative difference between water-leaving radiances denved by correction
method and the ones estimated from in-water measurements vs.
wavelength. ...............................................................................................
Figure 2.6-7
42
Example of spectra ncorded above surface, spectral water-leaving
radiance estimated from in-water measurements, and spectral waterleaving radiance derived by correction method. ........................................ 43
Figure 2.6-8
After correction: Comparison of remote sensing reflectance ratios
calculated from corrected water-leaving radiances and those estimated
frorn in-water measurements. .................................................................... 44
Figure 2.6-9
The correlation between slope fi (estimated from 670 nm band) and
variance of the surface signal measured above water in 412 nm band ......47
Figure 2.6- 10 The correlation between dope fi (estimated from 670 nm band) and solar
zenith angle. ..............................................................................................
48
Figure 2.6-1 1 The spectral biases of L, retrieved by correction method, that would be
introduced by existence of water-leaving radiance in 670 nrn band.,........5 1
Figure 3.4-1
Estimated contribution of atmospheric radiance to the upwelling radiance
measured from low-flying airplane ....................
Figure 3.4-2
.
.
................................. 65
The spectral ratios of diffuse to global downwelling irradiance as
calculated from clear sky irradiance mode1 used in correction for
overflights in the sunny conditions. .......................................................... 68
Figure 3.5-1
Before correction: Comparison of total radiance measured from airplane to
the water-leaving radiance estimated from in-water measurements ......... 75
Figure 3.5-2
After correction: Comparison of water-leaving radiance &(correction)
retrieved by correction method from aircraft radiance, and I , estimated
from in-water measurements.. ........................................................... 7
Figure 3.5-3
6
The deviations (biases) of water-leaving radiances derived by correction
method from the ones estimated from in-water measurements vs.
wavelength.. ...........................................................................................
Figure 3.5-4
7 7
After correction: Relative difference between water-leaving radiances
derived by correction method and the ones estimated from in-water
measurements vs. wavelength. ..................................................................
vii
78
Figre 3.5-5
Sunny day : Example of sea-surface spectra recorded from aircraft, spectral
water-leaving radiance estimated from in-water measurements, and
spectral water-leaving radiance derived by correction method ................. 79
Figure 3.5-6
Overcast day: Example of sea-surface spectra recorded from aircraft,
spectral water-leaving radiance estimated from in-water measurements.
and spectral water-leaving radiance denved by correction method .......... 80
Figure 3.5-7 Sunny days before correction: Comparison of remote sensing reflectance
ratios calculated from total airbome radiance to the ratios caicutated using
water-leaving radiance estimated from in-water measurements ............... 8 1
Figure 3.5-8
Sunny days after correction: Comparison of remote sensing reflectance
ratios calculated from corrected airborne data and those estimated from inwater measurements. ................................................................................. 82
Figure 3.5-9
Overcast days before correction: Comparison of remote sensing
reflectance ratios calculated from total airborne radiance to the ratios
estimated from in-water measurements..................................................... 83
Figure 3.5- 10 Overcast days after correction: Comparison of remote sensing reflectance
ratios calculated from corrected airborne dataand those estimated frorn inwater measurements. .................................................................................
Figure 3.5- 1 1 The spectral biases of
84
retrieved by correction method, that would be
introduced bv existence of water-leavinn radiance in 780 nm band. ........ 85
viii
List of tables
Table 2.5- 1
Optical measurements performed in equatorial Pacific. ........................... 27
Table 2.5-2
List of stations and conditions during measurernents.(equatorial Pacific) 28
Table 2.6- 1
The Root Mean Square Differences (RMSD) of uncorrected/corrected
radiances for each waveband computed with respect to the water-leaving
radiance estimated from in-w ater measurements. ..................................... 3 5
Table 2.6-2
The Root Mean Square Differences (RMSD) of unconected/corrected
remote sensing reflectance ratios computed with respect to the ratios
estimated from in-water measurements..................................................... 35
The relative errors in chlorophyll that are obtained by propagating errors in
R,(490)/Rm(555)through the SeaWiFS preliminary algorithm ................ 36
Table 3.4- 1
Conditions during aircraft flight over R N Miller Freeman, Bering Sea. .62
Table 3.5-1
Sunny day: The RMSD of uncomctedlcorrected radiances for each
waveband computed with respect to the water-leaving radiance estimated
from in-water measurements. ................................... .
.
.
.
............ 72
Table 3.5-2
Sunny day: The RMSD of uncorrected/corrected remote sensing
reflectance ratios computed with respect to the ratios estirnated from
in-water measurements.. .....................................................................
Table 3.5-3
.72
Overcast &y: The RMSD of uncomted/corrected radiances for each
waveband computed with respect to the water-Ieaving radiance estimated
from in-water measurements. ....................................................................
Table 3.5-4
73
Overcast day: The RMSD of uncorrected/correc ted remote sensing
reflectance ratios computed with respect to the ratios estimated from inwater measurements.
Table 3.5-5
.................................................................................
73
The relative errors in chlorophyll that are obtained by propagating errors in
R,(490) / R,(555) through the Bering sea empirical algorithm................ 74
The spectral distribution of light emerging from the ocean intenor, referred to as
ocean color, carries information about water composition, particularly about biologically
useful chlorophyll concentrations in the surface layer. When ocean color is measured
from a remote platform above the ocean (e.g. fiorn ship, aircraft or satellite) the signal
received by the sensor contains contributions from surface reflection and atmospheric
scattering in addition to the desired water-leaving radiance. In order to retrieve spectral
water-leaving radiance from the total signal, these unwanted contributions have to be
quantified and removed from the spectra by a correction aigorithm. The accuracy of those
aigorithms are critical for the reliability of the remotely acquired ocean color data
The main difficulty in correction of above-surface ocean color measurements for
surface glint is to account for the reflection of variable sky with randomly scattered
clouds from a rough sea. This work represents an attempt to constmct an operational
surface glint correction method for low-altitude remote sensing of ocean color that
applies for variable sky conditions. The method inuoduces diffise sky inadiance as the
key variable that is used in the sky-glint correction. The proposed surface-glint correction
method was successfully tested on data collected by a ship-mounted radiometer in the
equatorial Pacific, where the results derived by correction are compared with direct inwater rneasurements. The procedures necessary to correct low-flying aircraft data for
surface glint and atmospheric effects was assessed on dataset collected in the Bering Sea
from altitudes 150 - 300 m. After atmospheric correction, the sky irradiance estimated
from a clear sky mode1 was used in the sky-glint correction. The results demonstrate that
the low-altitude remote ocean color data collected under clear or variable sky conditions
can be accurately corrected for surface glint using measurements of diffuse sky irradiance.
List of symbols and abbreviations
Description
Unit
regression coefficients in pigment aigorithm
bidirectional reflectance distribution function
concentration of phytoplankton pigment
concentration of atmospheric constituent
regression coefficient in k algorithm (More1 1988)
p W cm-' nm-'
spectral global downwelling irradiance above
surface
spectral diffuse downwelling irradiance above
surface
pW cm-' nm-'
spectral direct downwelling irradiance above
surface
pW cm-'nm-'
spectral extraterrestrial solar irradiance
sr-'
ratio of sky glint and diffuse sky irradiance
degrees
field of view of the sensor
altitude dependence of atmospheric optical
thickness
altitude measured from the ocean surface
spectral diffuse attenuation coefficient for upwelling
radiance
spectral difise attenuation coefficient for pure
water
p W cm-' nm-' sr"
pW
nm-' sr-'
spectral radiance scattered by aerosols
spectral path radiance (scattered in the atmosphere)
p W cm-2nm'' sr-'
spectral radiance scattered by molecules (Rayleigh )
p W cm" nm-' sr-'
spectral sky radiance
pW cm" nm-' sr"
sky glint (spectrai sky radiance reflected from the
sea surface)
pW cm-2nm" sr-'
Sun glint (spectrd sun radiance reflected from the
sea surface)
p W cm" nm-'sr-'
total spectral radiance measured by remote sensor
p w cm" nm-'sr"
spectral subsurface upwelling radiance
'
pW cm-'nm- sr-'
spectral upwelling radiance just below sea surface
spectral water-leaving radiance
specual water-leaving radiance estimated from
in-water measurements
spectral water-leaving radiance estimated from
above-surface measurements
pW
nm-' sr-'
spectral water-leaving radiance in some red or nearinfrared spectral region
refractive index of sea water
refractive index of air (=1)
aerosol phase function
-sr-'
--
Rayleigh phase function
bidirectional reflectance distribution function
-
relative difference
root mean square difference
sr"
/ Ed
remote sensing reflectance = L.
-
transrnittance of the atmosphere
m
water depth
degree
angle between directions of incident and scattered
light
---
delta function
degree
the angle of the sensor relative to nadir
degree
solar zenith angle (SZA)
degree
Brewster angle
nm
wavelength
---
cosine of nadir angle of observation
m s-'
wind speed
---
Fresnel reflectance
reflectance of rough sea for variable sky (Aerosol)
--
optical thickness of the atmosphenc layer
degree
azimuth angle (relative to the Sun's azimuth)
---
regression coefficient in k aigorithm (Morel 1988)
sr
solid angle
---
aerosol single scattering albedo
xii
Acknowledgments
1 would like to tharik my supervisor Marlon R. Lewis for giving me the
opportunity to pursue my interests in remote sensing of ocean color, for support and
provision of al1 necessary resources. for involving me in beneficial field work
experiments, and for his encouragement to promote my work in international conferences.
1 thank my supervisory cornmittee members, John Cullen and Qiang Fu for their
constructive criticisrn and thought-inspiring comments of my work.
My gratitude goes to former and cumnt members of Biological Oceanography
Lab at Dalhousie, particularly to Aurea Ciotti for very helpful discussions and guidance in
various stages of work, Richard Davis for his assistance and Matlab tutoring, Jasmine
Bartlett for running atmospheric models; also to Yannick Hout as an extremefy helpful
neighbor, Daniela Turk as a sister in arms, Gary Maillet for help in laboratory
expenments, Juri Sildam for beneficial discussions, Xiaodong Zhang, J.P. Parkhill,
Barbara Nieke. Grazyana Tokarczyk, and Jim Christian. 1 would like to acknowledge Jeff
Wong for his help in aerosol models, Scott McLean from Satlantic Inc. for technical and
software support, and Nick Bond from NOAA for making complementary airborne data
available.
Finally 1 am very grateful to my farnily for their constant support and
encouragement, and al1 my fiends in Halifax, especially Maureen Cnbb, Christine
Pequigne, Sonja Novkovid and JoSko Bobanovie for help, advice and sharing the
experience. Special thanks goes to Jeff Scrutton for his invaluable support in al1 aspects
of my Iife and work.
xiii
Introduction
The spectral distribution of light emerging from the ocean interior, referred to as
ocean color, carries information about materials suspended and dissolved in the water.
The observation of the ocean surface from a remote platform above the sea in the visible
part of the spectrum (400 - 700 nm) is referred to as remote sensing of ocean color. The
main purpose of ocean color remote sensing is to remotely derive concentrations of sea
water constituents, such as dissolved organic matter, suspended sediments, and
paticularl y, chlorophy11 concentration in the surface layer (Clarke 1970). This is
biologically useful since chlorophyll is an indicator of dgal biomass and plays a central
role in the process of photosynthesis and primary productivity (Gordon 1980). The
quantitative assessrnent of marine phytoplankton production and the role of this
production for the possible storage of CO2 in the ocean is a critical environmental and
scientific problem (Gordon 1988). Remote sensing of ocean color makes it possible to
acquire information on the distribution of chlorophyll over large areas of the oceans in
short penods of time.
When ocean color is measured from a remote piatform above the ocean (e.g., from
ship, aircraft or satellite) the signal received by the sensor contains contributions from
surface reflection and atmosphenc scattering in addition to the desired water-leaving
radiance. In order to retrieve spectral water-leaving radiance from the total signal, these
unwanted contributions have to be qüantified and removed from the spectra. This process
is called correction of remotely sensed data for effects induced by the atmosphere and the
sea surface. Depending on wavelength, the surface reflection can contnbute over 50% to
the total signal measured from low-altitude platfoms (Austin 1974) and atmospheric
scattering up to 95% of the signal measured frorn high altitudes, i.e., satellites (Gordon
and Morel 1983 ). The correction procedures are, therefore, an integral part of ocean color
remote sensing, and the accuracy of these corrections is critical for reliability of the
remotely acquired ocean color data.
For measurements perfoxmed from Iow altitude, the atmospheric effect is reduced
to a minimum and the reflected sunlight and skylight from the sea surface represent the
main interfenng terms. At present, there are several methods for surface glint correction
which have k e n developed in respect to different conditions in which the remote
measurements are performed Le., clear or cloudy sky, Case 1 or Case II water (Austin
1974, Morel 1980, Bukata 1988, Mueller and Austin 1995, Lee et al. 1996). However, al1
of them require measurements of sky radiance in the direction appropriate for reflection
from sea surface into the field of view of the sensor. These measurernents are not
routinely made during remote observations. Especially for low-flying aircraft. often no
surface glint corrections are made at al1 (Kirk 1983), because the sky radiance is very
rarely measured during airborne ocean color sensing. This provided motivation to
construct an operational surface glint correction method for low-altitude platforms which
would not require sky radiance measurements.
In this work, the correction methods for shipbome and Iow-altitude airborne data
were studied. The objective was to constnict operational correction methods for these two
platforms which would not require sky radiance measurements and which would not be
sensitive to sky conditions (cloudiness). The surface glint correction method was
proposed and successfully tested on the data collected by ship-mounted radiometer in the
equatorial Pacific in January 1997, where the results derived by correction are compared
with direct, in-water measurements. The procedures necessary to correct low-flying
aircraft (150-300 m) data for atmospheric efiect were assessed on a dataset collected in
the southeastern Bering sea in A p d and May 1996.
In the first chapter, the physical and biologicai bases of ocean color and principles
of remote sensing are introduced. The second chapter deais with the shipbome rernote
sensing and surface reflection problem. In the first part, the theory of surface reflection is
described and the existing methods for surface glint corrections are reviewed. In the
second part the method for surface glint correction is proposed and tested on the data. The
third chapter includes corrections for low-flying aircraft. The theory of atmospheric
scattering is described, the existing methods are reviewed, the correction method is
presented and finally tested on the data. The fourth chapter is a bnef surnmary of the
work. The sun-glint mode1 by Cox and Munk (1954) is described in the Appendix A.
Chapter 1
1.1
Background
Ocean color
Ocean color refers to the spectral distribution of radiance leaving the ocean in the
visible part of the spectrum (400-700 nm) as seen at or just below the sea surface. It is a
result of backscattering of daylight from the ocean interior, from the sea water itself and
from the material suspended in the water. The sea water, phytoplankton, dissolved
organic matter, and suspended inorganic sediments absorb/scatter radiation in a spectrally
seIective manner and have characteristic effects on the spectnim of backscattered light.
Pure sea water absorbs strongly in the red which results in the deep-blue color of
oligotrophic waters (Smith and Baker 1981). hcreased concentrations of phytoplankton
(chlorophyl1) and its degradation products in more eutrophic regions change the water
color to green because of their increased absorption in blue part of the spectrum (Yentsch
1960). Abundant sediments and dissolved materiais from terrestrial sources in coastal
waters absorb in the bludgreen region and change the ocean color to yeIlow-brown. Thus,
the fact that the water composition is reflected by the color of the ocean provides a useful
tool for the remote sensing of in-water constituents.
In order to interpret ocean color in ternis of concentrations and types of dissolved
and particulate matter, a variety of bio-opticd algorithms have been developed (see
Gordon and More1 1983, O'Reilly et al. 1998). In the empincal approach, commonly used
in remote sensing, the ratio of water-leaving radiance at two wavelengths (or some other
combination) is statisticaily related to the concentration of the particular constituents
involved which are detennined by in situ measurements. The empincal bio-optical
algorithms for phytoplankton pigment make use of its increased absorption at the blue
part of the spectrum and are based on the bludgreen ratio of water-leaving radiances. as
first proposed by Clarke et al. (1970). Since then, biooptical dgorithms have k e n
continuously under refinement. The pigment concentrations retrieved by these algorithms
are more accurate for open ocean waters (-20%) han for productive and turbid coastal
regions (Gordon et al. 1988). The major goal of biologicai oceanographers is to develop
an algorithm which can achieve accuracy within 35% in estimating a wide range of
pigment concentrations (0.05
- 50 mg m-5 from opticd
measurernents (Mueller and
Austin 1995).
1.2
Water-leaving radiance
Water-leaving radiance, used in ocean color andysis, originates from subsurface
upwelling radiance that is transmitted through the watedair interface. The effect of
surface refraction and undenvater light field distribution on the magnitude and directional
properties of water-leaving radiance will be briefly reviewed in this section.
Refraction at the surface
Upwelling radiance below the surface consists of those photons which penetrate
the water body and are backscattered from the ocean intenor toward the interface. As the
upwelling light flux crosses the waterhir interface, it undergoes refraction at the
boundary. The refraction at the surface is described by Snell's law of refraction:
n, sin 8 , = n, sin 8,
(1.2-1)
where 8, and B.denote nadir angles in air and water respectively, na is index of refraction
for air (=l), and n, is index of refraction for sea water (=1.34). The consequence of
refraction at the surface is that ail radiance observed above the sea surface originates from
within the underwater cone of 48'. The upwelling radiance coming from nadir angles
8248" will be intemally reflected back in the ocean. Additionally, the radiance contained
within a small solid angle, Af&, below the surface will spread into a larger solid angle,
~ J ? ~ = n , ~ d [cos
n,
a./ cos@,], above the surface.
Angular distribution of upwelliig radiance
The upwelling radiance below the ocean surface generally does not forrn an
isotropic radiance field and the geornetricai structure of the field depends on the
illumination conditions (solar zenith angle) and bio-optical state of the water (Morel and
Gentili 1993, 1996, Morel et al. 1995). However, the simpliSing and commonly adopted
assumption in remote sensing is that the upwelling radiance is constant within a cone of
30" from nadir (Kirk 1983, Gordon 1988). Thus, isotropic underwater radiance within
cone of 30" will produce isotropic water-ieaving radiance that is spread to the 42" cone
above the surface. Therefore, the water-leaving radiance measured up to 42" from nadir
can be used to estimate nadir upwelling radiance just below the surface.
Transmission through the surface
Upwelling radiance just below the surface is related to the radiance just above the
surface by:
where p(&
directions
, 8,)
is the intemal FresneI reflectance for upwelling radiance for the
(a.,ea),and n,.
n, are indexes of refraction for sea water and air respectively.
Since n, varies only slightly with wavelength (Austin 1974, Gordon 1983), Lu and L,,
have essentially the same spectral composition. Austin (1980) has shown that, when Lu is
diffuse, the dependence of surface transrnittance, [I-p(& 8.)]/nW2,on wind speed is
weak, and he proposed the approximate transmitrance value of 0.544 for propagating Lu
through the sea surface.The relation, however, holds only for surfaces free of whitecaps.
To summaxize, subsurface upwelling radiance that is transmitted through the
water/air boundary changes magnitude and directional properties but not the spectral
distribution. The surface transrnittance in the absence of whitecaps does not depend on
wind speed. The water-leaving radiance measured within cone up to 42" from nadir is
uniform in distribution and can be taken as an estimate of nadir upwelling radiance jus<
below the surface. Finally, if the radiances are used through ratios, the ratio of water-
leaving radiances will be the sarne as the ratios of subsurface radiances (Gordon and
More1 1983).
1.3
Remote measurements of oœan color
The photometer used to measure ocean color above the cxean surface is usually a
radiance meter with a narrow field of view. Such a photometer, mounted at a remote
platform and pointed down at the ocean, can receive photons from four different sources
(Figure 1 -3-1):
from scattering of solar photons within the atmosphere (path radiance, Lp)
from reflection of the direct solar beam at the surface (sun-glint, L,,.,)
from reflection of difise skylight at the surface (sky-glint, LJbbg)
a
from scattering of solar photons below the surface (water-leaving radiance, L)
Atmosphare
.......................P..
Sea surface
8
I
Figure 1.3-1 The different origins of light received by a remote sensor pointed to the
ocean surface: L,, is path radiance (due to atmospheric scattering), LM, is sun-glint
radiance,
is sky-glint radiance, and L, is water-leaving radiance.
Sun
Sensor
Nadir
Figure 1.3-2 Definition of the angles involved in remote sensing: 0, is solar zenith
angle, 0 is zenith angle of the sensor (equal to nadir angle of the sensor), <p is azimuth
angle of the sensor relative to the Sun's azimuth.
The total apparent radiance t ,received by the sensor may be panitioned and expressed as
a sum of the contributions:
where A is wavelength, & is solar zenith angle, Ois nadir angle of the sensor. p is azimuth
angle of the sensor relative to the sun's azimuth (Figure 1.3-2). and h is altitude of
observation. The paîh radiance never maches the sea surface and increases with altitude
of observation. The second terni includes tsb,,,
Lsw,, and &, and represent the surface
signal which is transmitted through atmosphere to the sensor, where T(A8 hl is
transmittance of the intervening atmosphenc layer. Here, the water-leaving radiance is the
desired signal that contains information about the underwater light field, and water
composition. The essential problem in remote sensing, therefore, is to quantify the
emergent radiance in the presence of other light fluxes, i-e., to apply an efficient
correction aigorithm to remote measurements in order to retrieve spectral water-leaving
radiance from total upwelling radiance.
1.4
Platfonns for remote sensing
Ocean color can be measured directly just below the sea surface, or remotely from
a platform above the surface (ship, aircraft or satellite). The measurements performed
from a considerable distance above the ocean have an advantage that the information can
be obtained over a large area in a short time. However, each of the platforms provides
different surface resolutions, spatial coverage, and relative accuracies, and is suited to
sampling within specific spacdtime scales (Dickey 1991). The data acquired from
different platfoms are, therefore, often used in a complementary fashion to obtain
synoptic and accurate information in the region of interest (Smith et al. 1987).
Subsurface measurements of ocean color performed from ships provide accurate
point data about the underwater light field. Additionally, water composition and a wide
variety of parameters can be simultaneously measured from water samples. The
undenvater measurements are commonly used for bio-optical models and algorithm
development (Morel 1988, Gordon 1988, Gordon and Morel 19831, but also as surfacetmth data for calibration and validation of aircraft or satellite products (Gordon et al.
1983). The disadvantage of in-water measurements is their limited spatial coverage and
coarse spatial sarnpling which cannot provide a synoptic survey of large regions.
Measurements performed above the surface by a ship-mounted radiometer pointed
at the surface provide continuous monitoring of ocean color dong the ship track. Such a
system represents an extremely slow moving, low-altitude remote sensing device.
However, total radiance measured above the surface contains a contribution from surface
reflection in addition to the desired water-leaving radiance. The data have to be corrected
and the accuracy of those corrections are critical in retneval of
L.Since surface water
samples can be taken simultaneously with remote measurements, such a data-set c m be
also utilized for bio-optical modeling (Carder and Stewart 1985, Bukata et al. 1988). The
spatial coverage is, however, limited to the ship track.
Airbome remote sensing has many advantages. It provides rapid horizontal
monitoring of ocean color, measurements of the sarne area can be repeated on time scales
of hours or days so that temporal variability can be studied, and the measurements can be
performed in cloudy conditions. The aerial coverage is generally limited to coastal and
near shore regions and data are acquired dong the aircraft's linear track. Spatial coverage
increases with aititude but so does the contribution of atmospheric scattering and more
accurate corrections are needed.
Satellites provide relatively less accurate data but provide a synoptic view of two
dimensiond spatial structure of large areas, and a wedth of horizontal detail impossible
to obtain
from ships and aircraft. Furthemore, it is possible to obtain low frequency time
series (repeat observations at 1 day and more) over long penods of time (10 years and
more) and the data can be obtained from isolated locations inaccessible to ships and
aircraft. The disadvantage of satellites is that they are unable to view cloud covered
ocean, the high frequency temporal coverage is limited, and finally, very accurate
atmospheric corrections are needed in order to retrieve surface signal from the signal
rneasured outside the earth's atmosphere.
Chapter 2
2.1
Shipborne remote sensing
Measurement of ocean color above the surface
Measurements perfomed a few meters above the surface by a ship-mounted
radiometer require comction for reflection of Sun and sky light from the sea surface only.
because the effect of atmospheric scattering may be considered negligible. The
transmittance of an atmospheric layer a few meters thick may be set to unity and the total
spectral upward radiance L,is then given by :
Since the reflection at the surface does not depend significantly on wavelength
(Austin 1974), the spectral composition of the reflected sky and Sun light will be equal to
those of the downwelling sky and Sun radiation. The direct solar radiation covers a large
spectral range, and sun-glint will contribute in al1 wavelengths. Diffuse downwelling sky
radiation, on the other hand, is comprised predominantly of shorter wavelengths.
Therefore, sky-glint will alter more the blue part of the spectrum. An example of spectral
distribution of diffuse and direct downwelling irradiance is shown in Figure 2.1 - 1.
The magnitude of sky-glint and sun-glint present in the upwelling signal depends
largely on the angle of observation and on the solar zenith angle. Sun-glint dominates
over a region around the mirror angle of reflection (0 = Os and qz = 180") and its spatial
distribution depends on the wind speed. Sky-glint is dways the dominant factor when
observing near the horizon up to a nadir angle from 68O to 23". depending on azimuth
160
1
1
1
1
1
140
-
-
120
-
-
100-
-
n
P
E
=
I'
E
O
3
a
Y
a
O
c
a
.u
.-
80
-
solar zenith angle 32
-
O
-
60-
Wl
C
.-
40-
s
a
G
O
n
20
difiuse
V
-
O
O
400
I
1
1
1
1
450
500
550
wavelength [nm]
600
650
700
Figure 2.1-1 Spectral distribution of direct Sun and d i f i s e sky irradiance on a clear day.
Measurements are performed at nine wavebands. The d i f i s e irradiance was measured by
bIocking the solar disc to the radiometer (Biospherical MER 1010). The direct irradiance
was
obtained as a difference between total and diffuse irradiace. The data are from
equatorial Pacific, January 1997.
angle and solar zenith angle (Plass et al. 1976). In this region. the color of the ocean is
detennined largely from the color of the sky as refiected by the surface. By pointing
radiometer at small nadir angles and away from the sun-glint pattern, surface glint can be
minimized and water-leaving radiance will dorninate the signai. However, surface glint
will still be present in the signal and will have to be removed by a correction algorithm.
2.2
Surface reflection
The reflection of radiance from the sea surface is a radiative transfer problem and
can be described formally in ternis of a bidirectional reflectance distribution function
(BRDF).The reflected radiance is related to the incident radiance as:
where index i denotes incident and r reflected direction and f? is solid angle. The quantity
r(B,,g
+Or, pr) specifies the BRDF of the surface (or radiance reflectance function) and
depends only on the nature of the surface (Mobley 1984). For the calm ocean surface
BRDF can be expressed in terrns of the Dirac delta function (6) as:
where p(4) is the Fresnel reflectance of water for an incident angle 8, . That means that
for a given direction of incidence there is only one direction ailowed by laws of
reflection. The radiance reflected from a calm sea surface is related to incident as:
L r ( e r * ~ r=) P('~)L;
('i*c~i)
(2.2-3)
The reflection from a rough surface is more complex and difficult to describe
analytically. Xn a case of wind roughened sea surface. the BRDF describes the reflection
from a collection of individual wave facets and is treated by numerical methods (Mobley
1994, Preisendorfer and Mobley 1986). The approximate expression for the BRDF
(Gordon and and Wang 1992, Takashima 1985, Raschke 1971) includes equations for
Fresnel reflectance and surface slope statistics derived by Cox and Munk (1954) where
the probability of surface inclination is given by a Gaussian distribution dependent on
wind velocity (see Appendix A).
The effect of a rough surface is that the radiance coming from particular direction
will be reflected within an angular region surrounding the specular direction. This angular
region will increase with wind speed. The BRDF posseses the reciproçity property, which
means that the location of the source and sensor may be interchanged (Strum 1981). To
evaluate directional radiance reflected from rough sea, the angular distribution of incident
radiance has to be known and then the integral (2.2-1) can be solved numerically.
2.2.1 Reflection of sunlight from the surface
Downwelling solar radiance incident on the ocean surface c m be approximated by
a direct beam, and its directionality can be expressed as:
L ,(844 =
-@,)6(g>- O , )
(2.2-4)
where B, and p, are solar zenith and azimuth angle respectively. For a flat ocean the direct
solar radiance will be refiected only in the mirror direction which is determined by the
Sun's position (Equation 2.2-3). In the case of a rough sea, sun-glint is given in terms of
the BRDF of the surface. Introducing direct Sun radiance from (2.2-4) into the integral
(2.2- 1) and perfonning integration we have:
Lsu,-,(@*<p)=~ , , ( @ , ~ ~ , ) r ( @ , , g >&<pJ
~
(2.2-5)
The commonly used expression for the BRDF is the one given by Cox and Munk (1954)
as a function of wind speed, solar zenith angle. and observation geometry (more detailed
description is given in Appendix A). A strong sun-glint in general occurs in the solar
plane around the specular direction and is spreads more widely with increasing wind
speed. In the plane perpendicular to the solar plane (which is recommended for remote
measurements) the sun-glint is less pronounced and covers a smaller angular region. The
problem of sun-glint can be largely avoided by appropriate choice of sensor geometry,
time of remote measurements, sea state condition and direction of viewing.
2.2.2 Reflection of sky light from the surface
in the case of a fiat ocean, the sky-glint received by the sensor will come from one
particular specularly reflected point in the sky, whose radiance can be easily measured
(Equation 2.2-3). In contrast, the skylight reflected from the wind-roughened ocean
surface into the FOV of observer will come from an angular region surrounding the
specularly reflected point (Figure 2.2-1). The sky-glint received by a sensor is then a
convolution of the sky radiance in that angular region of the sky and the statistical
distribution of wave slopes at the point of observation on the surface. The sky-glint of a
rough sea is associated with a BRDF of the sea surface and the integration in (2.2-1 ) is to
be taken over Sn sr of incident solid angle
a..The
numerically if the distribution of sky radiance is known.
integral (2.2- 1) can be solved
Figure 2.2-1 Reflection from a rough sea surface. In the case of a calm sea surface, for a
given direction of incidence there will only be one direction allowed by laws of reflection.
In the case of rough sea surface, the acceptance angle R of a sensor is increased due to the
refiection from wave facets which nomals deviate from vertical (dashed-dotted lines);
increases with wind speed. Sky-glint received by sensor is a convolution of the sky
radiance in the solid angle observed in the glint, Ls&l), and the statistical distribution of
wave slopes at the point of observation on the surface.
Cox and Munk (1955) evaluated the directional se-glint (in relative units) for
smooth and rough surfaces and for three cases of sky conditions: a hypotheticai unifom
sky, a clear sky, and a completely overcast sky. They came to the following conclusions:
( 1 ) For a nadir angle of observation, sky-glint does not depend strongly on wind speed
and angular distribution of sky radiance, and the surface reflectance is equai to the Fresnel
reflectance value for a calm sea (0.02). (2) For observation angles relevant for remote
sensing (up to 40' from nadir) the surface refiectance for uniform sky is not greatly
influenced by surface roughness (increases about 5%). (3) For clear and overcast
conditions the surface reflectance of rough sea may be lower or higher than the one of a
smooth sea, depending on angular distribution of sky radiance. For example, for nadir
angle 30". the sky-glint of a rough sea in a clear day is 20% higher than that of a calm sea.
Saunders (1968) showed that the effect of varying surface roughness on the amount of
glint is smaller than the effect of varying sky conditions. The sky condition (Le., the
distribution of sky radiance) is, therefore, the essential parameter in determining the
precise extent to which sky light is reflected by a rough air-water interface (Bukata 1995).
However, if the portion of the sky reflected into the FOV of the sensor is
approximateiy uniform in distribution, and the angle of observation is close to nadir, the
reflected sky radiance will not be greatly affected by wind speed. Under these conditions
the sky reflection from the rough surface can be regardeci as if the surface was calm
(Austin 1974), and Fresnel reflectance values can be used. The approximately uniform
sky radiance distribution cm be found on a clear day in the region of minimum of sky
radiance, Le., in the solar vertical plane at an angular distance approximately about 90"
frorn the Sun.
2.3
Review of existing methods tor surface glint correction
The standard procedure for surface glint correction, recommended in protocols for
SeaWiFS validation (Mueller and Austin 1995). suggests that measurements of total
upward radiance from the ship are perfonned in clear sky conditions. The radiometer
should point to the surface with an angle of about 20" from nadir and away from the sun's
azimuth by at l e s t 90°, i.e., to the point with the minimum in specularly reflected sky and
Sun
radiance. The protocols recommend that the spectra should be recorded with high
frequency (at least 2Hz) so that temporal sun-glint outliers can be removed from the
steady background signal before calculating finai mean spectra. For these mean spectra,
the glint generated at the surface is due to the reflected skylight only. On a clear day, the
angular distribution of the sky radiance in the portion of the sky observed in the glint cm
be taken as approximately uniform- Therefore, the surface reflectance will be not greatly
influenced by surface roughness, and the sky-glint can be computed using Fresnel
reflectance and measurements of sky radiance (Equation 2.2-3). This method performs
weIl for clear sky but can be ais0 applied to the uniforrn overcast conditions, and requires
measurements of sky radiance in the direction appropriate for specular reflection.
One commonly used approach for surface glint correction makes use of the fact
that clear water can be regarded as 'black' in the red or near infrared region of the
spectrum, Le., that L,,,(redlir) is approximately zero (Gordon 1981). That means that the
signal received in the red or near infrared region represents solely a measurement of the
specularly reflected radiation. It is then possible to extend this over the whole spectrum
by using the measured wavelength dependence of the incident radiation (More1 1980). If
the sensor is directed outside the Sun glint region, the surface glint will be due to the
reflected skylight only, and can be calculated according to:
Lx&?.-,
(A9,e) =
L, (red /ir. 8.cp)
L* (A. 0. Q) + a)
L, (red Ar. 0. g, + n)
where Lrh(A,8.4)+x) is sky radiance measured at the sarne plane, and at a zenith angle
equal to the nadir angle of L,(A, 6?p), and where L,@(re&ir. 8.QH z) and L&ed/ir, 6 9) are
appropriate values in the red or near infrared region. Estimated sky glint is then
subtracted from the total signal in order to recover
L.However,
the assumption that
L.(redir)=û is only valid for waters displaying small to moderate concentrations of
suspended sediments. Increases in the amount of suspended particles, including
phytoplankton, will increase the backscattering coefficient of the water and, therefore.
L.
at al1 wavelengths where particles do not absorb strongly (Kirk 1983). Increases in L, are
particularly obvious in the near infrared bands, and in the case of turbid water the black
ocean assumption cannot be applied (Bukata 1995).
Bukata et. al. (1988, 1995) describe a method for surface glint correction of
radiances collected on lakes by a nadir-viewing ship-mounted radiometer ( M ,@). ~ h e
total radiance observed above the surface is expresseci in terms of spectral diffuse and
direct downwelling irradiance at the surface as:
L,(A.e = O. cp = O) = Edb ( A ) + f2 Ednn (A. O , ) + Lw(A. 0 = 0. (P = 0 )
(2.3-2)
The first term in (2.3-2) represents the sky-glint and the second represents the sun-glint.
The factor fiis the ratio of sky-glint radiance to the downwelling diffuse sky irradiance.fi
is the ratio of sun-glint to the downwelling solar irradiance, Edfl is the downwelling sky
irradiance. and EdirCC,
is the downwelling dircct irradiance from the sun located at a so1ar
zenith angle 8,. In the case of a relatively calm lake surface. the fraction fi may be
expressed as:
where po is the Fresnel reflectance for vertical incidence. LSi(A,O0) is the spectral zenith
sky radiance. The ratio Ls&,OO)/Edi&)
is spectrally dependent and was determined from
Ls&ilOO)and E d A ) measurements. The fraction of direct sun irradiance reflected from
the surface in the FOV of the sensor fi, could be computed assuming that water-leaving
radiance in the near infrared band is zero. Alternatively (in the case of turbid waters), they
suggested the complete avoidance of sun-glint by choosing appropriate time for
observation and surface condition. For nadir view. these optimal conditions include solar
zenith angles ranging frorn 40"-65", and wind speed up to 5 m s-'. The measuremenis
necessary for correction are difise and global sky irradiance and zenith sky radiance.
Lee et al. (1996) recently proposed a correction procedure which can be applied
for variable sky conditions. To account for nonuniform sky reflected from the surface into
the sensor. they partition measurements of downwelling sky radiance into Rayleigh and
aerosol components. The Rayleigh component, which is due to scattering by molecules in
the atmosphere. is assumed to be constant in the effective solid angle of the sky observed
in the glint and is removed using appropriate Fresnel reflectance value. The aerosol
component includes cloud effects and varies greatly in the portion of the sky responsible
for the glint. Its contribution can be removed only by finding the proper reflectance value
m.
The method used to estimate
p~
is an optimization aigorithm. in which the
pararneterization for remote sensing reflectance R, (in terms of in-water absorption and
backscattering coefficients) is compared with Rayleigh corrected experimental data. The
method uses measured spectral shapes of particle absorption coefficients from surface
sarnples as input into the refiectance parameterization, and then, by minimizing the e m r of-fit between R, remote sensing data and R, parameterization, it derives contributions
from surface reflection, and inherent optical properties at the same time. The method was
tested for clear and turbid water conditions, and performed well in botb cases. However,
it requires measurements of sky radiance and additional measurements of the particle
absorption spectrurn from a surface water sample.
2.4
Proposeci method for surface glint correction
Al1 of the existing rnethods for surface glint correction described in previous
section require measurements of sky radiance in the direction appropriate for reflect ion
from the surface into sensor (Motel 1980, Mueller and Austin 1995, Bukata 1988) or inwater optical properties (Lee et al. 1996). These measurernents are not available in Our
data sets and are difficult to obtain on a routine basis from ship, buoy. and aircraft .
ptatforms. Therefore, 1propose a method for surface glint removal using measurements of
diffuse downwelling sky irradiance only. The advantage of the method is that it
incorporates the effect of clouds. The technical advantage is that the global and diffuse
sky irradiance can be measured with a sarne instrument: an upward viewing radiometer
where the diffise component can be determineci by blocking the Sun disc to the
radiometer. Thus, EAA) and Edi-A)CM be continuously monitored during remote sensing
observations.
For the sun-glint correction 1 adopted the procedure from the protocols for
SeaWiFS validation (Mueller and Austin 1995). The protocol recommends that the sunglint is minimized during measurements by pointing the radiometer to the surface outside
the sun-glint pattern, i.e., in the pfane perpendicuiar to the solar plane. If the spectra are
recorded at least 2 times per second, the temporal sun-glint outlien can be removed from
the steady background signal by rejecting the values falling more than 1.5 standard
deviations from the mean. Thus, the final mean spectrum is free of sun-glint contribution
and incorporates the glint due to the reflected skyiight oniy. It is given by:
The sky-glint correction is based on my assumption that the sky glint is
proportional to the diffuse sky irradiance and can be expressed as:
The factor fidepends on observation geometry (nadir angle of the radiometer 8,azimuth
angle of the radiometer relative to the Sun q ~ ) sky
,
conditions (which are influenced by
solar zenith angle B, and cloudiness) and sea state (wind speed v) but does not depend on
wavelength. By setting fito be spectrally constant, 1 assumed that the spectrd distribution
of sky radiance which is reflected into the field of view of the sensor, is equal to that of
diffuse sky irradiance. The rationale for that assumption is that the skylight reflected into
the sensor from a rough surface may corne from a large effective solid angle R (Figure
2.2- 1 ) where R increases with surface roughness. Ultimately, the spectral distribution of
the portion of the sky reflected in the sensor can be approxirnated with the spectral
distribution of sky irradiance ( =
h.
LSb(12)(cosûldR) . Furthemore, if the clouds are
present in the portion of the sky reflected in the glint, the spectral composition of skyglint will be a mixture of the cIoud base radiance with solar spectrai properties ('white'),
and the background spectral Rayleigh sky radiance ('blue'). fhese spectral variations of
downwelling skylight will be automatically integrated over the sky dome by using
spectral diffuse sky irradiance.
Using the proposed sky-giint parameterization, Equation 2.4-1 can be rewritten as:
Assuming that water-leaving radiance in some red or near infrared band approximates
zero, the signal received in that band is due entirely to sky-giint and Equation (2.4-3)
becomes:
L,(red/ir)= f, x Edg ( r e d / i r )
(2.4-4)
The factor fisets the scaie for the reflection, i.e., it represents an estimate of the extent to
which EdidÂ) is reflected from the rough sea surface, and can be determined for each
measurement as:
L, (red / i r )
fi = E d -(red / ir)
Water leaving radiance is then computed by inserting flfrom (2.4-5) into (2.4-3) and
subtracting the sky-glint from total signal:
Lf (red / ir)
Lw(A) = Lt ( A )- Edw (red /ir)
Edig
(4
The proposed surface glint correction method requires the existence of a spectral
band in red or near infrared portion of the spectmm for which L, approximates zero. In
the case of clear open ocean water (Case 1 water, with chlorophyll concentration less than
0.25 mg m-)), the assumption L(670 nm)=O can be used (Gordon 1981). For al1 other
Case 1 waters, the wavelengths 765 nm and 865 nm should be considered for correction
(Gordon and Wang 1994). For Case II water, the assumption L(1012 n m ) 4 was found
to be appropriate even in a case of waters heavily loaded with sediment (Bukata 1995).
2.5
Data and Methods
2.5.1 Data
Ocean color data were collected in January 1997 in the equatorial Pacific from
R N Kaiyo at 9 stations. This region is characterized as the clearest water in the world's
oceans. The opticai measurements performed are listed in Table 2.5-1. A11 the
measurements were made simultaneously. The profiles of L,(L z), starting at 3 m depth,
were measured at the rate of 6 Hz at nominal fa11 speeds of 1 ms-', which results in 6-7
data samples per meter. Lt(A) was collected at a frequency of 6 Hz for 5 minutes with a
Satlantic Profiler viewing the sea surface from the deck of the ship. The L,(i.)
measurements were performed approximately 90' away from sun's azimuth and the nadir
angle of observation for al1 stations is Iisted in Table 2.5-2. The EAR) spectroradiometer
was mounted on the deck and the measurements were made in sequence with EdidR).
which was measured by blocking the direct Sun irradiance i.e. by shading the Sun's disc
to the radiometer. Al1 the sensors have a bandwidth of 10 nm. In addition to the optical
measurements, a suite of meteorological parameters including wind speed, sky conditions
and cloud observations were collected as well as chlorophyll sampies in the surface layer.
The list of stations and conditions dunng the measurements are shown in Table 2.5-2.
Optical meenwments
Profi le of subsurface
spectral upwelling radiance
U s 2)
Spectral total radiance
above the surface &(A)
Downwelling spectral
irradiance E&)
1
Wavebands [ml
I
Instrumentation
406, 412, 443, 470, 490, Satlantic Profiler
510, 520, 555, 565, 620,
(OCR-20)
665,670,683
406, 412, 443, 470, 490, Satlantic Profiler
510, 520, 555, 565, 620,
(OCR-200)
665, 670, 683
I
-
410, 441, 465, 490, 507, Biospherical MER 1010
520, 532, 550, 565, 589, spectroradiometer
671, 765
-
Diffuse downwelling
spectral inadiance E d A )
410, 441, 465, 490, 507, Biosphericd MER 1010
520. 532, 550, 565, 589, spectroradiometer,
Lazin occulter
67 1, 765
-
Table 2.5-1
Optical measurements performed during expenment. Al1 the radiometers
have bandwidth of 10 nm.
Station
Date
Latitude
1 Longitude 1
no.
1
Jan, 10
3N
172'30'E
-
---
Solar zeni !h
angle
34"
1
Skv conditions
-
I
Uadir angle of Nind [ms-'1
radiometer
cirrus 9110
cumulus 1110, zenith -clear
2
3
Jan. 11
Jan. 12
scattered cumulus 2110
1
4
1
1
Jan. 13
flying
- - close to sun
scattered cumulus 3110
hazy, flying clouds
5
Jan. 14
O
173' 53'W
1
6
Jan. 15
O
25"
1
170" 34'W
variable sky: cirrostratus 2110
1
29"
scattered cumulus 2110
zenith clear,little hazy
cumulus and cirrostratus on
7
Jan. 16
O
.
horizon 1/10
167" 48'W
27"
cirrostratus 10110
flying cumulus 4110
8
Jan, 17
thin cirrus 10110
flying cumulus 4110
9
Jan. 18
flying cumulus 5/10
_j
Table 2.5- 2 List of stations and environmenial conditions during meüsureinents in January 1997 .
2.5.2 Water-leaving radiance
Water-leaving radiances were estimated from i,,,(A, z ) profiles measured at the
stations and by the correction of simultaneous above-water rneasurements. The first
procedure includes extrapolation of upwelling radiance measured at the depth z to the
0-11 and propagation of Lu@-)
point just below the sea surface [i.e., computation of
across the sea surface [Le.. computation of L,,,(O>]. The radiance just below the sea
surface &,(A, 03 is related to the radiance at the depth t according to equation:
L,(1.0~)
= Lu(A, z ) exp[k(A)z]
(2.5- 1)
where &(A, z ) is the upwelling radiance at depth z and k(A) is the spectral attenuation
coefficient for upwelling radiance. The natural logarithm of Equation 2.5- 1 is of the forrn:
,
l n [ ~ (A,
, z)] = I ~ [ L(&O-)]
-k ( Â k
(2.5-2)
in this linear system, the least-square regression fit of In[L,,(R z ) ] with the depth z gives
the values for dope k(A) and intersection Lu(A, O-). Thus, the k(R) and L,(A, O-) cm be
automaticaily determined as a part of a fittïng procedure. The assumption required is that
k(A) is constant within the depth range under consideration Le. that the incident
downwelling irradiance just below the surface is constant during measurements. In the
regression (2.5-2), the data points within the fint 10 m of the profile are used in fitting
procedure (6 datapoints per meter). FinaIly, the upwelling radiance just below the surface
L,(A, 0')was propagated across the surface using relation proposed by Austin (1974):
L~(&O+ ) = 0.544 L,(A.O-)
(2.5-3)
The water-leaving radiances estimated from subsurface measurements were taken as
surface-tmth data for validation of the correction method.
In order to retrieve t,frorn above-surface radiances, the surface glint correction
described in section 2.4 was applied to the data The temporal sun-glint outliers were
removed from the high frequency L, signal, and the final spectra were calculated as
averages over 2 min intervals. The water-leaving radiance was computed from (2.4-6)
assuming that L ( 6 7 0 nm) is equal to zero. According to Gordon ( 1981) and Gordon et ai.
( 1983) this
approximation can be applied in Case 1 water with chlorophyll concentrations
less then 0.25 mg m". Here, the 670 nm band was chosen for correction because (a) it
was the reddest band common to the ai1 radiometers (b) the measurements are perfonned
in clear water with chlorophyll concentration 4 . 2 5 mg m" and. (c) L ( 6 7 0 nm) estimated
from in-water measurements was found to be sufficiently small (see discussion).
The wavebands used in the analysis were the ones common to both sensors
(Profiler and Ed spectroradiometer). For the first 5 stations, the five common wavebands
were 443, 470, 520,565, and 670 nm; for the last 4 stations four more bands were added
(4 12,490, 5 10, and 555). The 2-5 nm difference bctween Ed and
Lucentrai wavelengths
in 4 bands were corrected by shifting the &centrd wavelengths using linear interpolation
between two closest Ed datapoints.
2.5.3 Remote sensing reflectance and chlorophyll algorithm
Remote sensing reflectance is computed as a ratio of L, estimated from both
a b o v e h l o w surface rneasurements to the downwelling imadiance
the surface as:
EAA) measured above
Since the blue-green ratios of remote sensing refiectance are ofien employed in empirical
chlorophyll algorithms (Gordon and Mord 1983, O'Reilly et al. 1998)- the ratios
cornmonly used in those algorithms are calculated. In examining influence of errors in
retrieved R, ratios using the correction method to the chlorophyll estimate, 1 considered
the SeaWiFS prelirninary empirical bio-uptical algorithm (O'Reilly et ai. 1998). The
algorithm relates chlorophyll concentration C to R,(490)/ R,(555) ratio using a modified
cubic polynomial equation:
where R=log[R,(490)/
R,(555)],
a=-0.04, al=0.34 1. ar=-3.00 1, a3=2.8 1 1, and
a ~ 2 . 0 1.4 The algorithm is designed for wide range of chlorophyll concentrations.
2.5.4 Statistical tests and errors
The quantities retrieved by the correction method (L,and Rn)are compared to the
ones
estimated from in-water measurements. The root mean square differences (RMS
relative error) are calculated according to:
(,.[
mm =
-
1 X(correction)- X(in water)
X(in - water)
i'1"
The bias was calculated as:
Bias = X(correction)-X(in-water)
The relative differences (errors) were calculated as:
RD=
X(correction) - X(in - water)
X(in - water)
The erron in reflectance ratios, dR. were propagated numerically to pigment estimation
using the chlorophyll algorithm fiom Equation (2.5-5) where the error in chlorophyll is
given by:
2.6
Results and discussion
2.6.1 Results
The total radiance measured above the surface, t l ( A ) , before correction, and
&(A,)&(&)
ratios calculated from uncorrected data were compared with those
estimated from in-water measurements (Figure 2.6- 1 and Figure 2.6-2; Table 2.6- 1 and
Table 2.6-2.). The plots illustrate the necessity for corrections since the surface reflection
in troduces large scattering of datapoints, increases the magnitude of the measured signal,
and influences the spectral distribution of L,(A.). The R,(AI)A?,(&)
ratios for the
uncorrected data are significantly lower than the ones estimated from in-water
measurements (Figure 2.6-2) and the chlorophyll concentrations derived from uncorrected
data would be, in general, overestimated. Particufarly, the Rm(490)/R,(555) was
underestimated by 34.4% which would overestimate chlorophyll retrieved by SeaWiFS
pigment algorithm by 75.4% (Table 2.6-3).
Before applying the correction to the data, I tested my assumption that sky glint is
linearly related to diffuse sky irradiance. The sky glint was calculated as a difference
between surface radiance L,(A) corrected for sun-glint outliers and water-leaving radiance
L,+.(A)estimated from in-water measurements. The sky-glint was related to the diffuse sky
inadiance measurements via linear regression, LsQ,=fI
Ew (Figure 2.6-3). The average
R' for al1 measurements was 0.9. The linear relationship is preserved regardless of sky
conditions and sea surface state (which are listed in Table 2.5-2), which supports the
assurnption that the spectral distribution of sky-glint can be approximated with the
spectral distribution of sky irradiame. The slope /i, however, changes for each
measurement due mainly to the different sky conditions (see discussion).
Water leaving radiance obtained by the correction method, L(correction), was
compared with the vaiues estimated from in-water measurements, &.(in- warer), in Figure
2.6-4. The correlation coefficient between L,,,(correction) and î&(in-water) was 0.96,
which shows a very good linear relationship between L, derived by correction and the
one estimated from in-water measurements. Depending on the wavelength, the RMSD for
water-leaving radiance ranges from 10% to 20% (Table 2.6-1). The plot of biases versus
wavelength (Figure 2.6-5) shows that the method tends to overestimate L, in the blue and
green part of the spectrum. However, the relative errors for each spectra are consistent
with wavelength (Figure 2.6-6), which means that the method produces approximately
constant relative errors in al1 wavebands for each measurements. The best-fit linear
regression for relative errors shows that the method on average tends to overestimate &by 7% (Figure 2.6-6). Since the dope of the regression is 10" nm-', the relative errors
tend to be constant with wavelength. This fact is very useful in retrieving remote sensing
reflectance ratios Rrr(AI)/'Rn(&), because the relative enor of the ratio is given by:
Therefore, if the L, in different bands can be retrieved with same relative errors, these
errors will came1 out in a ratio. For that reason the remote sensing reflectance ratios are
more robust to corrections, as indicated by the excellent agreement of the R, ratios
retrieved from corrected data and those calculated using L, from in-water measurements
(RMSD for al1 ratios is within 8%). Particularly, the R,(490)/ R,(555) ratio was retrieved
with 3.8% RMSD, which. when propagated to chlorophyll, gives 7.7% RMSD in the
estimation of pigment (Table 2.5-3). This is much lower than the inherent accuracy of the
pigment algorithm. In order to achieve accuracy in pigment retrieval within 2 0 8 in clear
water [R,(490)l R,(555) > 2 ] the errors in R,(490)/ R,(555) should be less than 10%.
The proposed correction method meets the required accuracy of reflectance ratio retrieval
from above-surface measurements.
Tabk 2.6-1
The Rmt Mean Square Differences (RMSD) of uncorrected/corrected
radiances for each waveband computed with respect to the water-leaving radiance
estimated from in-water measurements.
- -
Remote m i n g
reflactanm ratio
-
RMSO %
(before correction)
RMSD 96
(aftw correction)
# of datapoints
% (555)
34.4
3.8
5
R, (443)/ R, (555)
33.7
3.9
5
I
Rs(490)
Table 2.6-2
The Root Mean Square Differences (RMSD) of uncorrected/corrected
remote sensing reflectance ratios computed with respect to the ratios estimated from in-
water measurements.
---
-
-
Corrected data
SeaWiFS prellminary
algorithm
Estimated from From above
in-water
surîace
measurements measurements
Relative
difference %
IRMSD = 34.4%
Table 2.6-3
Estimated
Ch1 [mg/ml
Chl relative
enor %
Derived by
corrections
I
Relative
Estimated
ditference % Ch!(mglm7
1
RMSD = 3.8%
Chl relative
error Ob
Stctistics for uncorrectcd and correctcd data. The relative difference in Rm(490)/R,.,(555)are calculüted with respect to
the values estimated from in-water measurements. The chlorophyll concentration was computed using uncorrectcd/corrected ratios.
The relative errors in chlorophyl l are obtained by propagating relative differences in R,(490)IR,s(555) through the SeaW iFS
preliminary algorithm (Equation 2.5-5).
1.6
A
-
80
O
7L
1.4-
a
cn
E
1.2t
a
=Y
s1.
Y
0.8
-
443 nm
470 nm
490 nm
510 nm
520 nm
555 nm
565 nm
670 nm
O
A
rt
O
*
V
+
O
-0.2
O
0.2
0.4
0.6
0.8
Lw (in-water) [ P W
1
1.2
nm" s i '
1.4
-
-
-
1.6
1
Figure 2.6-1 Before correction: Cornparison of total radiance measured above the
surface Lr(above-sutfiace) to the water-leaving radiance estimated from in-water
rneasurements &(in-wnter). The wavebands are indicated by di fferent symbols.
Figure 2.6-2 Before correction: Cornparison of remote sensing reflectance ratios
R,(A,)I Ru(&) calculated from the total above-surface radiance Ars ratio(ubove-sutfiace)
to the ratios calculated from water-leaving radiance estimated from in-water
measurements Rrs ratio(in-water). The ratios cornmonly used in pigment algorithms are
indicated by different symbols.
Figure2.6-3 Relationship between sky-glint LSQ,,
and d i f i s e downwelling sky
irradiance Edw Sky-glint was computed as the difference between total radiance
measured above the surface L , and L,estimated from in-water measurements. Example
data are plotted for three sets of measurements. Wavebands are indicated by different
symbols. Sky-glint was related to the Edg via linear regression: Lsb.pflEdifl(solid 1ines).
Line 1: 6+27O, wind 10 m s", scattered cumulus 3/10, R- 0.9 1 ; Line 2: 8p27°. wind 8
m s-l, cirrostratus 10/10, scattered cumulus 4/10. R ~ 0.92;
= f i n e 3: 0 ~ 3 2 "wind
.
2m
S.'.
clear, ~ ' = 0 . 9 8 .The linear relationship is preserved for al1 9 measurements with average
R' of 0.9. Thar means that spectrum of Lsb, can be approximated with the spectral
distribution of Edw The slope.fi, depends mainly on the variability of sky conditions. All
measurements are made approximately 36" from nadir and 90° away from solar plane.
Lw (in-water) ( k W cm
-2
nm
-1
sfl ]
Figure 2.64 After correction: Cornparison of water-leaving radiance &.(correcrion)
retrieved by the correction method from total radiance measured above the surface, and
L.((in-\vater) estimated from in-water rneasurements. Measurements are performed at 9
wavebands which are indicated by different syrnbols. The correlation coeffkient is 0.96
and root mean square error is 0.08 p W cm" nm-' sr-'.
waveiength [nm]
Figure 2.6-5 The deviations (biases) of water-leaving radiances derived by the
correction
method L,&orrection)
from L&n-water),
estimated from in-water
measurements vs. wavelength. The dashed line indicates the best fit linear regression
through the points. The dotted line is 95% confidence interval for the regression line: the
correction method tends to overestimate L, in al1 iiexcept 555 nm and 565 nm bands.
The 95% confidence interval for the slope includes 0: the biases are not spectral
dependent.
500
wavelength [nm]
Figure 2.66 Relative difference (Equation 2.5-8) between water-leaving radiances
derived by the correction method LJcorrecfion), and L(in-water) estimated from inwater measurements vs. wavelength. The data from each measurement are connected with
a solid line. The dotted line represent the best fit linear regression through al1 points. The
relative differences are approximately constant with wavelength for each specuum; the
slope of the regression is IO-' nm". The method tends to overestimate L, by
approximately 7%.
January 16
Lt (above-surface)
Lw (in-water)
Lw (correction)
wavelength (nm]
Figure 2.6-7 Example of spectra recorded above surface, L,(above-su>fnce). spectral
water-leaving radiance estimated from in-water measurements &(in-warer), and spectral
water-leaving radiance derived by the correction method from the L,,L(correction). The
error bars on L, represent the variance of mean spectra caiculated from high-frequency
measurements (introduced by reflection of variable sky from rough sea surface). These
variances are propagated to correction). The data are from January 16, wind 8 md.
variable clouds (conditions listed in the Table 2.5-2).
1
Figure 2.6-8
1.5
2
2.5
3
3.5
Rrs ratio (in-water)
4
4.5
5
After comction: Cornparison of remote sensing reflectance ratios
R,(A,)I &(A2) ccalulated from comcted water-leaving radiances Rrs ratio(correction)
and those estimated from in-water measurements Rrs ratio(in-water). The ratios
commonly used in pigment algonthms are indicated by different symbols.
2.6.2 Discussion
The proposed surface glint comction method is based on my assumption that the
sky glint is linearly related to d i f i s e sky irradiance (Equation 2.4-2). From there, the
dope fiis constant with wavelength and is given by:
r, (0s.e.(P)=
tSbl
(A.0 J $0.P)
Edi* (A*8 s )
and is different for each rneasurement. The easiest way to explain those variations is by
considering a flat sea surface. In that case, the sky-glint received by a sensor will come
from one particuîar specuiarly reflected point in the sky, and then the slopef, is given by:
If the sky is uniform (EdH = n Lsb),
and angle of observation is within 20° from nadir
( ~ 0 . 01)2the slopef, would be given by fi= p / x = 0.0067 sr-'.
If the sky radiance is not uniform in distribution, the slope fiwill depend on the
ratio of sky radiance in the particular direction to the diffuse sky irradiance. The ratio
Lrk./Edg is called normalized downwelling radiance and has units of sr" (Harrison 1988,
Walker 1994). For a fixed angle of observation (pconst), fl depends only on the
intensity of normalized sky radiance in that particular direction 8,and
For angles of
observation relevant to remote sensing (&O0-40". p 9 0 - 1Bo0), the sky radiance obsewed
in the glint will come from zenith region 0°-40" and azimuth about 90°-180° away from
Sun. The normalized sky radiance in this region will increase as the Sun approaches zenith
(Harrison 1988). Therefore,
fi
will increase with solar elevation (solar zenith angle
decreases).
The intensity of downwelling skylight can also increase if randomly scattered
broken clouds are present in otherwise clear sky (Kirk 1991). Due to increased scattering
by the clouds compared to molecular scattering, the radiance of the scattered cloud is
greater than radiance of a surrounding clear sky (Saunders 1968). Therefore, if the bright
cloud is observed in the glint, fiwill accordingly increase.
The sarne reasoning should hold in the case of the rough sea. Now, the sky-glint is
given in tems of BRDF (Equation 2-24), and expression forfl(2.6-2) becomes:
r, (e.P,es)= 2K
Ed&
0s)
In this case. the random interface wilI reflect a large angular region of the sky into the
sensor. if that portion of the sky contains scattered clouds, the background sky and cfoud
x reflected alternatively from the dynamic wave facets. That will introduce
radiance will l
variance in the surface signal, which can then be used as an estirnate of sky variability.
Since presence of bright clouds should increasefi, the correlation between variance of the
surface signal and fl is expected. At the same time fi should increase with solar zenith
angle decreasing.
The best correlation (~~=0.67)
was observed between fi and the variance of the
total surface radiance in the 412 nrn band (Figure 2.6-9) where f i tends to increase with
variance of the surface signal. The 412 nm band was chosen because of the pronounced
cirrus 911 0 cumulus 1/IO; 3 mls
clear sky; 2 m/s
scattered cumulus 211 0 ; 4 m/s
scattered cumulus 311 0 hazy; 8 m/s
cirostratus 2/10 cumulus 2/10; 9 mls
cumulus and cirostratus 1/ I O ; 9 mls
cirostratus 10/10 cumulus 4/10; 8 m/s
thin cinus 10/10 cumulus 411 0; 8 m/s
cumulus 5/10; 9 mls
fl(uniform sky,flat sea)=0.0067
O
0 .O5
0.1 5
O .2
variance of the signal a; 41 2 nm
O. 1
0.25
0 -3
Figure 2.6-9 The correlation between dope f~ (estimateci from the 670 nm band) and
variance of the surface signai measured above water in 412 nrn band. The stations are
indicated by different symbols. The sky conditions and wind speeds during measurements
are listed in the legend. The circle represents the theoretical value for flat surface and
uniform sky. The dashed line is the best fit linear regression for measured datapoints
(~'=0.67).The linear regression has intercept 0.0068 sr", which agrees with the predicted
value. The variance of the signal is produced by reflection of variable sky from a random
sea interface.
-
c i m s 9/1 O cumulus 1/1 O; 3 m/s
clear sky; 2 mis
scattered cumulus 2/10; 4 m/s
scattered cumulus 3/10 hazy, 8 mls
cirostratus 2110 cumulus 2110; 9 rnls
cumulus and cirostratus 1/10; 9 rnls
cirostratus 10110 cumulus 4110; 8 m/s
thin cirrus 10/10 cumulus 4110; 8 mis
cumulus 5110; 9 rnls
25
30
solar zenith angle [degrees]
35
Figure 2.6-10 The comlation between the slope fi (estimated from 670 nm band). and
solar zenith angle. The stations are indicated by different syrnbols and sky
conditionslwind speed dunng measurements are listed in the legend. The dashed line is
the best fit linear regression for measured datapoints. The correlation between solar zenith
angle is weak (~'=0.35) and the dope is small (-0.001[sr degreel-'). However. the
tendency of decreasing fi with solar zenith angle increasing can be obsewed. The
scattering of datapoints is probably induced by the variability of sky conditions (scattered
clouds).
contrat between blue sky and white clouds. The variance of the surface signal contains
information about sky variability and sea surface state. However. in previous studies
(Saunders 1968) the effect of varying surface roughness on the arnount of glint is seen to
be smaller than the effect of varying sky conditions, therefore the increase o f f , cm be
attributed largely to the increax of sky variability. The dependence of fi on the solar
zenith angle is shown in Figure 2.6-10, where fitends to decrease as solar zenith angle
and
) the siope of the regression
increases. However, the correlation is weak ( ~ ~ d . 3 5
small (-0.001 srd'degree-'). It appears that the solar zenith angle has some effect in
changing the fivalue, but this effect is difficult to quanti@ because of small range of solar
zenith angles considered and the sky-state eHect (clouds). There was no correlation
observed between fi and the nadir angle of observation, mainly because the observation
geometry was very similar in ail measurements. However, the exact values off, can be
evaluated numericaily (Eq2.2-1) only if the full distribution of sky radiance is known.
Here the factor fi was derived assuming that the water-leaving radiance in the 670
nm band equals zero and that the total radiance in that band is due to surface glint.
According to Gordon (1981), this assumption is valid for Case 1 waters with chlorophyll
concentrations 4 . 2 5 mg m". However, L,,,.(670nm) is never equal to zero. Even in pure
sea water there is smail contribution due to Raman scattering (Bartlett 1996). The
presence of chlorophyIl in the water results in additional elastic and inelastic scattering
(flourescence at 685 nm) which both influence the 670 nm band (Bartlett 1996). Another
contribution may corne form scattering by bubbles (Zhang et al. 1998) and sediments
(which are not likely to be present in open ocean waters). Thus, if the assumption
L ( 6 7 0 n m ) S is violated [i.e. u 6 7 0 ) = L(670)
+ Lsb-g(670) ]
the
fi values (and the
surface glint) would be overestimated, leading to consistent underestimates of
L..
The
spectral biases which would be introduced in ntrieved L, by actual existence of L(670)
are shown in Figure 2.6- 1 1. The biases were computed for LJ670)=0,0.0 1, 0.05, 0.1 and
0.2 pW cm" nm-l sr". For the data considered in this experiment. the typical L,,.(670) was
0.01 p W cm" nm-' sr", and the consequent negative biases would represent only -3%
relative error in the typical observed
L..
By
increasing &.(670), the biases would
consequently increase as the method is found to be very sensitive to the actual magnitude
of &.(670). However, in the case of this experiment perfomed in very clear open ocean
water, the assumption that L ( 6 7 0 nm)=û is acceptable andfi values estimated from 670
nrn band seem to perform well for sky-glint correction. For al1 other case 1 waters, the
wavelengths 765 nm and 865 nm should be considered for correction (Gordon and Wang
1994), while for Case II water the waveband centered at 1012 nm was found to be
appropriate even to a waters heavily loaded with sediment (Bukata 1995).
The uncenainties of
L.estimated from subsurface profiles are expected to be very
low (within 5%) because (a) the emor introduced by instrument self-shading was
estimated to be less than 1% in blue and less than 3% in the green part of the spectrurn
(Gordon and Ding 1992), (b) the casts are perfomed at the period of steady direct sun
(variability in incident irradiame was rninimized), (c) the ship shadow was avoided
according to SeaWiFS protwol. Additionally, the profiles were smooth and the average
R' for the regression (2.5-2) in propagation of the underwater signai to the surface
0.97.
was
waveîength [nm]
Figure 2.641 The spectral biases of L, retrieved by correction method that would be
introduced by existence of water-leaving radiance in 670 nm band. The magnitude of
L(670 nm) for which the biases are computed is indicated in the legend. The biases are
computed for a typical signal by propagation of the error in the 670 nm band through
correction method to the rest of the spectnim. The existence of L(670 nm) results in
consistent underestimates of &.-
Another possible source of error in comparing L, derived from above and below
surface measurements is related to anisotropy of the underwater light field. and actual
bidirectional reflectance of the ocean. As pointed out by More1 and Gentili (1996), the L,
estimated from remote measurements at a particular nadir and azimuth angle cannot be
taken as an estimate of L,,.in vertical direction; L(8, p) may be lower or higher than
LJB=OO). This depends on observation geometry (8, p), illumination conditions (solar
zenith angle Os, and the relative proportion between direct Sun and diffuse sky irradiance),
wavelength, and the bio-optical state of the water body (depicted b y Ch1 in Case 1 water).
Using Monte-Carlo simulations, they showed that for the typical geometry considered in
this experiment (Mo,
@O0, 8,=30°), and with chlorophyll concentration of 0.1 mg
m", and clear sky, the & ( M o , p=9û0) revieved from above-surface measurements
should be multiplied by factor 0.91-0.95 (depending on wavelength) to produce an
estimate of L(B=O"). This can explain the trend of &(&40°, p=90°) retrieved by the
)
form in-water
correction being on average 7% higher than ~ ( M Oestimated
measurements (Figure 2.6-5 and Figure 2.6-6). However, the bidirectional correction is
recommended only in retrieving absolute values of &, because the ratios L.(RI)IL,,,(&)or
R,(Rl)/R,(A2)
are weakly afTected by the angular effect issues. The bidirectiond
correction is not considered in present analysis because the correction factors available
represent only a rough approximation of the conditions experienced in this experiment.
2.7
Conclusion
A new method for surface glint correction of low-altitude ocean coior data was
presented. The method requires high frequency measurement of the sea surface radiance
(for the sun-glint correction) and measurements of spectrai diffuse downwelling sky
irradiance (for the sky-glint correction). The sky-glint correction is based on the
assumption that the spectral distribution of sky radiance, which is reflected into FOV of
the sensor, is equd to that of diffuse sky irradiance, Le., that the sky glint is proportional
to the diffise sky irradiance. The assumption was tested on the data and is well founded.
Furthermore, the corrections account for the effeçt of variable sky reflected from the
random sea interface, which usuaily represents the main difficulty in correction of abovesurface measurements. It was found that the proposed correction method is not strongly
influenced by clouds, variability of sky conditions, and sea surface state. However, the
existence of a spectral band for which L, in the red or near infrared portion of the
spectrum approximates zero places a restriction on the waters for which this correction
method is applicable. In the case of clear water with low chlorophyll concentration (as in
this experiment) the utilization of 670 nm band is found to be adequate.
The proposed method is applied to 9 spectra, each of which are recorded from
above the sarne water type but in different environmental conditions. It gives very good
results for water-leaving radiance retrieval from above-surface measurements, and
excellent results in Rn ratio retneval from corrected data. Unfortunately, the sky radiance
was not measured during the expriment
and, therefore, the cornparison with other
methods on the sarne dataset was not possible. Because of a limited number of datapoints,
the method needs further validation.
Chapter 3
3.1
Airborne remote sensing
Measurements of ocean color f rom aircraft
The magnitude of upwelling spectral radiance sensed at altitude h by a radiometer
pointed at the sea surface is given by the generai form of the radiative transfer equation
(1.3-1). The signal contains contributions from atmospheric scattering, and surface
reflection, in addition to the desired water-ieaving radiance. The total radiance scattered
in the atmosphere (path radiance
4 ) can
be partitioned into a sum of independent
contributions due to molecular scattering (Rayleigh radiance L,) and scattering by
aerosols (aerosol radiance L),
as:
Here. the notations follow the definitions from section 1.3. This partitioning assumes a
sufficiently thin atmosphere, so that the single scattering approximation can be applied
with no interaction effect between air molecules and aerosols (Gordon 1987). The path
radiance increases drastically with altitude of observation. The first problem connected
with the atmospheric correction of data remotely sensed at different altitudes is the
definition and evaluation of the absorption and scattenng processes due to atmospheric
constituents as a function of flight altitude. The second problem involves surface glint
correction.
3.2 Atmospheric constituents and processes
3.2.1 Atmospheric attenuation
The attenuation of solar radiance by absorption and scattering as a function of
wavelength is defined through the opticai thickness of atmospheric constituents. The
main constituents affecting radiance in the visible and near-infrared wavebands are
permanent gases and aerosols (which are associated with scattering), ozone and water
vapor (which are associated with absorption at certain wavelengths). Since the data from
aircraft are generaily taken at a selected altitude, the extinction processes have to be
defined as a function of the specified altitude. If $(Am) is total atmospheric optical
thickness of the constituent i at wavelength A, then the optical thickness of the
atmosphenc layer between the sensor and the surface for that particular constituent can be
written as:
f i( A ho) = H,(hO)si
(A. =)-
(3.2- 1 )
where Hi(ho) expresses the dependence of atmospheric optical thickness on altitude ho
above the surface. If the vertical distribution of concentration c,(h) of each atmospheric
constituent is known, Hi(h0) can be obtained through the relation:
The parameterization of ~ ( A wand
) Hi(ho) for permanent gases, ozone and water vapor.
in ternis of meteorological parameters can be found in Guzzi et al. (1987) and references
within. In contrast, the aerosol optical thickness cannot be parameterized because the
aerosol is highly variable in time and space, and is, in general, unknown in remote
sensing experiments. Aerosol optical thickness can be evaluated either from models
(Shettle and Fenn 1979), or deduced from the remote sensing data itself as an unknown
during iteration procedures of a correction algorithm ( G u u i et al. 1987, Zibordi 1988). or
by direct measurements (Maracci and Zibordi 1990).
The optical thickness of the atmospheric layer due to al1 constituents is given as a
sum of individual q(R, ho):
~ ( î . . h , ) = ~ R ( ~ . h , ) + ~ , ( l i , h o ) + ~ , ( h h , ) + ~ , , ( h h , ) (3 -2-3)
where subscripts R, A, W,and O3 stand for Rayleigh, aerosol, water vapor, and ozone
respectively. The total transmittance of the atmospheric layer between the sensor and the
sea surface is defined as:
T(A1 h,) =ex~[--r(Ah,
)/PI
where p is the cosine of the nadir angle of observation.
3.2.2 Rayleigh scattering
Scattering by air molecules is described by Rayleigh theory. The theory is based
on the assumption that the scattering particles are smdl (diameter cc A), spherical. and
that the particles scatter independently of one another. The Rayleigh scattering is
wavelength dependent and varies proporiional to x4. The radiance scattered by molecules
in the atmosphere below the sensor which enters a remote sensing device at altitude h
(Rayleigh path radiance) can be written as (Bukata 1995, Guui et al. 1987):
Here, sn (Ah) is the spectral optical thickness of the atmospheric layer between sea
surface and altitude of observation h associated with Rayleigh scattering, E d A h ) is soiar
downwelling irradiance incident on altitude h, T is transmittance of the intervening
atmospheric layer that accounts for absorption (ozone, water vapor), PR is the Rayleigh
phase function, and p is cosine of nadir angle of observation. The Rayleigh phase
function (normalized to 4%)gives angular distribution of scattered energy:
where y is scattering angle between the direction of incoming direct solar radiation and
the direction of light scattered into the remote sensing device. The impact of Rayleigh
scattering c m be readily predicted since the principles of Rayleigh scattering are well
established and the concentration profiles of atmospheric gases with altitude are known
(Gordon 1992, Bukata 1995).
3.2.3 Aerosol scattering
The scattering by atmospheric particles is described by Mie theory. In contrast to
Rayleigh scattering, the aerosol scattering has little wavelength dependence, especially
when the particle size relative to the wavelength is large (McCartney 1976). The radiance
scattered by aerosol in the atmosphere below the sensor (aerosol path radiance) c m be
written as:
where subscript A refers to the aerosol equivalent of the Rayleigh parameters in the
equation (3.2-S), and
is the aerosol single scattering albedo defined as a ratio between
scattering and attenuation. The radiative transfer parameters for aerosols [TA,o~and PA1
are detennined by the size, shape, refractive index and concentration of aerosol particles
in the intervening atmosphenc layer. Since the aerosol is highly variable in time and
space. proper calculations would require measurements of multispectral aerosol optical
thickness rA(k),which can be performed using a sun-photometer. From the measured
rA(k),one can deduce the aerosol particle size distribution (King et al. 1978). Using
assumptions about particle shape and refractive index, Mie theory can yield reasonable
estimates of
OA and
PA,and radiance scattered by aerosol can be computed. However, the
aerosol optical thickness is not routinely measured during remote sensing observations.
The estimation of aerosol scattering mostly relies on models, and rernains the largest
uncertainty in the remote sensing of ocean color (Gordon 1978).
3.3
Existing methods for atmosphetic correction
Although airborne remote sensing of ocean color is widely used in detection and
measurements of phytoplankton abundance, the methodologies for aircraft data correction
are still challenging. The main reason is that very few parameters necessary for proper
correction are commonly measured during airborne remote sensing campaigns. Ln order to
minimize and eliminate the atmosphenc effect, the measurements are often perfoxmed
from very low altitude (100 rn or less), and sometimes the corrections are not made at al1
(Hoge et al. 1986, Harding et al. 1992). Uncorrecteci ocean color data have been shown to
be correlated with differences in chlorophyll concentrations and have been used to
qualitatively assess distributions of phytoplankton (Clarke 1970). In order to utilize
aircraft data in quantitative analysis and bio-optical aigorithms, or for validation of
satellite products, the airbome ocean color data have to be comcted for atmospheric and
surface glint effects.
The standard procedure xecommended in protocols for SeaWiFS validation
(Mueller and Austin 1995), suggests that the airbome measurernents are performed under
either clear skies or a completely uniform cloud cover. The data measured under variable
cloud conditions are very difficult to correct and interpret because the area on the sea
surface viewed by the radiometer is often illuminated differently than is the incident
irradiance sensor at the aircraft, and sky radiance incident on the surface also varies
unpredictably. For flight altitudes less than 100 m. the atmospheric effect can be
completely neglected; for altitudes of 100
-
3 0 m, the atmospheric layer can be
considered transparent (trammittance is close to 1) but the path radiance should be
evaluated through the models (Guui et al. 1987). The sun-glint should be avoided
completely by choosing the time of remote observation and flight direction, and sky-glint
should be removed using sky radiance and Fresnel reflectance (Equation 2.2-3). However.
sky radiance coming from directions appropriate for reflection from the surface into the
sensor is often not measured during remote observation. Its estimation from models is
very difficult even under ideal clear sky, and is wholly impractical under variable cloud
cover. Under clear sky conditions sometimes a typical spectral distribution of sky
radiance is taken from the literature and used for sky-glint correction (Hoge et al. 1987).
One attempt to eliminate skylight reflection from the surface makes use of a
phenornenon called polarization by reflection. The Iight reflected from the surface is
completely polarized (with electric field vector paraltel to the surface) when the angle
between the reflected and refracted beam is 90°. The angle of incidence at which this
occurs is determined by the index of refraction of the water (n, = fan &) and is called
Brewster angle & (for the ocean & =53"). At Brewster angle, the light reflected from the
sea surface has a prefemd horizontal polarkation, even in the case of rough seas (Sydor
1997). Therefore, if the measurements are performed at Brewster angle in conjunction
with polarïzer, the surface glint can be largely eliminated during measurements (Clarke at
al. 1970, Neville and Gower 1977, Borstad et al. 1980).
Findly, the correction methods can be completely based on a radiative transfer
model. The model proposed by Guzzi et ai. (1987) is based on an approximate solution of
the radiative transfer equation and includes the effect of multiple scattering. The model
was successfully validated on data taken from aircraft at different altitudes (Zibordi and
Maracci 1988; Zibordi, Parmiggiani and Alberotanza 1990; Zibordi, Maracci and
Schlittenhard 1990). However, the radiative transfer models are often too complicated for
operational use.
3.4
Data and Methods
3.4.1 Data
Remote ocean color data were collected from a low flying NOAA P3 aircraft in
the southeastern Bering Sea in April and May 1996. Airborne upwelling nadir radiance
L,(A) and downwelling global irradiance EAR) were measured with a Satlantic SeaWiFS
Aircraft Simulator (SAS-m. The instrument collects data at seven spectral bands, 10 nm
wide, centered at 4 12,443,490,555, 670, 683 and 780 nm. Optical data were sarnpled 10
times per second, averaged over 1 s, and merged with navigational instruments. A suite of
meteorological parameters was collected during the flights. Sbipboard observations of
upwelling radiance 45 cm below the sea surface were made at the same wavebands, using
a Satlantic Tethered Spectral Radiometer Buoy (TSRB)deployed from the R N Miller
Freeman during aircraft overflights. Chlorophyll samples, collected at the same time.
were analyzed fluorometrically aboard the ship. A total of five flights were analyzed:
three under fairly clear sky conditions, and two under overcast skies. The list of
overflights and environmental conditions are shown in Table 3-4- 1.
3.4.2 Computation of water-leaving radian-
Water-leaving radiance was estimated from spectral subsurface upwelling
radiance measured at 45 cm depth. The in-water signal was prnpagated to the surface
using the attenuation coefficient k(R) computed from measured chlorophyll values, C.
according to (Morel 1988):
k(A) = kW ( A ) + x c (A)ce(')
(3.4- 1)
The kw(A) represent spectral values of attenuation coeffkient for pure water. The
coefficients ~ , ( h and
) e(X) are tabulated values taken from Morel (1988), which were
detemined by statistical analysis of the k(R) in Case 1 water. The spectral upwelling
radiance just below the surface &,(A,O-) was computed according to Equation 2.5-1. with
z=0.45 m. Water-leaving radiance was obtained by propagation of Lu(AO') across the
water-air interface using the relation proposed by Austin (1974), according to Equation
2.5-3. The calculated water-leaving radiances are taken as surface truth for validation of
the correction method.
,
3.4.3 Atmospheric and surface glint correction
In order to obtain a simplified correction algorithm for low flying aircraft, the
contribution of each terni in Equation 1.3-1 to the total radiance is estimated using the
following methods.
Aerosol scattering
The radiance scattered by aerosols in the atmospheric layer between sea surface
and aircraft was computed according to (3.2-7). The aerosol phase hinction PAused was a
two-term Henyey-Greenstein function, with parameters for marine aerosol proposed by
Gordon et al. (1983). The aerosol optical thickness r~ is estimated from a model for
aerosol extinction in a marine boundary layer (Wong 1996, Winter 1994). The model
cakulates the size distribution of sulfate aerosol as a function of measured relative
humidity, and from there, the extinction coefficients, and single scattering albedos. In the
case of flight altitudes 150 - 300 m, the radiance scattered by aerosol was estimated to be
an order of magnitude less than the measured signal and therefore was neglected.
Rayleigh scattering
The radiance scattered by molecules was calculated according to (3.2-5).The
molecular phase function used was the classical Rayleigh function (3.2-6). Molecular
optical thickness
m, as
a function of flight altitude, was obtained through relations
proposed by Van Stokkom and Guui ( 1974):
r R(A.h ) = H R( h ).0.0088A~-'~~-'"
where
-
H R ( h )= 1 - e x p ( 4 . l l88h 0.00116h2)
IA(clm)I
[h(km)]
It was found that Rayleigh scattenng contributes in the blue part of the spectrum and
therefore cannot be neglected.
An exarnple of estirnated atmospheric spectral radiance (Rayleigh and aerosol)
together with the total airborne signal and water-leaving radiance estimated from in-water
measurements is shown in Figure 3.4-1.
A tmospheric trammittance
The amospheric transmittance for upwelling radiance is calculated from the
optical thicknesss <A, h) of atmospheric constituents according to Equation 3.2-4. The
absorption optical thickness of water vapor is estimated using spectral absorption
coefficients of water vapor (Leckner 1978), measured temperature, due point temperature,
relative humidity, and parameterization of the venical profile of absolute humidity (see
Zibordi et. ai. 1988). However, the water vapor absorbs only slightly in the visible
wavebands used in this analysis. The absorption optical thickness of ozone was estimated
using spectral absorption coefficients of ozone (Leckner 1978), ozone concentration for
Benng Sea from climatological data, and the parameterization for the venical distribution
of the ozone concentration (Iqbal 1983).
The maximum attenuation of the upwelling radiance in the atmospheric layer
berween airplane and sea surface was estimated to be 2%. The absorption optical
thickness of water vapor and ozone for the atmosphenc layer between the sensor and sea
surface was estimated to be extremely low and negligible. Therefore the atmospheric
layer was assumed to be transparent and the atmosphenc transmittance was set to 1.
Figure 3.4-1 Estimated contribution of atmospheric radiance to the upwelling radiance
measured from low-flying airplane: radiance scattered by molecules (Rayleigh) and
radiance scattered by aerosol (Aerosol). The total upwelling radiance, Ldabove-surface),
and water-leaving radiance estimated from in-water measurements L,,,(in-water) are
plotted for cornparison. (April23, sunny conditions, flight altitude 294 m)
Correction method
Using the simplifying assumptions from previous section, (1 -3-1) becomes:
For our overfiights (solar zenith angle
- No,wind speed 6 ms-', and nadir view of
sensor), the probability of seeing the direct sun-glint was estimated from the Cox and
M u n k mode1 (1954, Appendix A) and found to be very low
(-
IO-' ). Additionally, the
possible temporal sunglint outliers were removed from the data before calculating final
mean spectra (method described in section 2.4). Therefore, for Our overflights, the effect
of direct sun glint was neglected. This led to the simplified working equation of the fonn:
which includes radiance scattend by molecules in the atmosphere (Rayleigh scattering)
and the diffuse skylight reflected from the sea surface as the unwanted contaminations
which have to be removed.
The Rayleigh radiance was computed according to (3.2-5) and the sky glint was
removed by the method proposed in section 2.4. assuming that L, at 780 nm is zero.
Water-leaving radiance was calculated as:
Since downwelling diffuse irradiance was not measured during the flights. it was
estimated in one of two ways. For sunny conditions. Ed#
measured downwelling irradiance EAA) as:
was calculated from
where the spectral ratio of diffise to global irradiance [EdidR) / EAA)] was calculated
from a solar spectral irradiance m d e l for the clear sky (Gregg and Carder 1985). The
mode1 uses the following input parameters: solar zenith angle, pressure, temperature, dew
point temperature, relative humidity, wind speed, visibility, and ozone scale height. The
meteorological data used as input parameters are measured on the aircraft. For the ozone
scaie height, the climatological data for that region were
used. The spectral ratios
[Ed,~R)/E&)] computed by the mode1 for the time of ovemights are shown in Figure
3.4-2. For the completely overcast sky, al1 of the measured global irradiance was assumed
to be diffuse.
3.4.4 Chlorophyll algorithm
The chlorophyll algorithm considered here is the local Benng sea empirical
aigonthm developed by Cullen at al. (1998). The algorithm relates chlorophyll
concentration to the remote sensing reflectance ratio Rm(490)/R,(555). It is a modified
cubic polynomial of the sarne form as SeaWiFS preliminary algorithm (Equation 2-55)?
but with coefficients
--a4
empirically adjusted to the local conditions (a0 =-0.437,
a = O S 2 1 , a2=- 1.238, a3=0.6516, and a4=- 1 648). The errors in Rn(490)/R,(555)
retrieved by the correction method are numencally propagated through the algorithm in
order to assess their influence on the chlorophyll estimate (Equation 2.5-8).
Bering sea, April23, sunny
O .4
I
I
1
I
1
1
I
Figure 3.4-2 The spectral ratios of difise to global downwelling irradiance as
calculated from clear sky irradiance mode1 (Greg and Carder 1985). These ratios are used
in estimating diffise downwelling irradiance for the time of overflights in the sunny
conditions.
3.5
Results and discussion
In order to evaluate the effectiveness of the correction method in retrievd of L,,.
and remote sensing reflectance ratios from aircraft data, the uncorrected and corrected
values are cqmpared with the ones estimated from in-water measurements. Since diffuse
sky irradiance was estimated differently for sunny and overcast days, the analysis was
conducted and results are discussed for each condition separately.
3.5.1 Comparison of radiances
The comparison of total radiances, LJA) before correction with those estimated
from in-water measurements &(A) for both sunny and overcast days, are shown in Figure
3.5-1. The measured signal is higher than the surface-tmth due to the surface reflection
and the relative increase varies with wavelength. For sunny day the R M S D for
uncorrected Li(A) with respect to &(A) range from 129% in the blue to 42% in green
wavebands (Table 3-54);in other words, L, represented 40%
- 70% of the total signal.
For the overcast day. the R M S D are much higher (Table 3.5-3)and L, (which was very
low) represented only 20% of total radiance.
Comparison of water-leaving radiance obtained by the correction method,
LJcorrection), with the values estimated from in-water measurements L,,.(in-water) for
both sunny and overcast days, is show in
Figure 3.5-2.The correlation coefficient
between L,,.(correction), and &(in-water) was 0.99 which shows their excellent linear
relationship. The biases are small (Figure 3.5-3) and the corrections significantly lowers
RMSD of L, retrieved by comtion in comparison with surface truth (Table 3.5-1 and
Table 3.5-3). However, the best fit linear regression through biases show that the method
in general tends to overestimate L,in blue wavebands and underestimate in the green part
of the spectrum. The examples of spectral radiances for sunny and overcast day are shown
in Figure 3.5-5 and Figure 3.5-6.
3.5.2 Sunny conditions
For sunny &y, the correction mettiod gives an estimate of L, in blue and green
wavebands on average within 10%. The biases are small, but the relative errors (Figure
3.5-4) show an increase in the blue relative to the green wavebands. That indicates chat
.
either the modeled Edfl used for sky-glint correction, does not exactly represent the
spectrum of glint, or that estimated radiance scattered by molecules in the atmosphere
was
incorrect. In the estimation of Rayleigh scattenng 1 used the optical thickness
Q
computed as a function of altitude only (3.4-4 and 3.4-5). However, if r~ is computed
from pressure difference between sea and aircraft level (Strum 1981). the results for
are about 15% higher than the ones used in this work. This possible increase of Rayleigh
scattering could account for some of the spectral effect observed in relative errors.
The differences in magnitude of relative errors in L, in difierent wavebands
induce errors in the remote sensing reflectance ratio R,(XI)/R,(h2)- If the L, in different
bands is retrieved with same relative error, these errors will cancel out in a ratio
(Equation 2.6- 1). For corrected data the relative errors in L, are not consistent with
wavelength which results in a relative error in R,&)/R,(L2)
(Table 3.5-2). On the other
hand, the relative mors for uncorrected data remain approximately constant in 490 nrn
and 555 nm band (not shown). That means that the glint alters equally both bands, and the
glint effect cancels out in ratio. The effect of glint on R,(490)/Rm(555) ratios depends on
the actual magnitude of this ratio i.e., on the chlorophyll concentration. For the high
R,(490)/&(555)
ratio (low chlorophyll) the ratios computed from uncorrected above-
surface data would be underestimated. For low R,(490)/Rn(S55) ratio (high chlorophyll)
the ratios computed from uncorrected above-surface data would be overestimated. When
R,(490)lR,(555)
is close to 1, the glint effect would cancel out in ratio, and the ratios
computed from uncorrected above-surface data would be close to the actual
Ru(490)/R,(555) ratios, as observed in Benng S e a The &(490)/&(555) ratios for
uncorrected data agree better with the ones estimated from in-water measurements (0.8%
RMSD) than Rn(490)/R,(555) derived from corrected data (6.8% RMSD).Consequently,
the error in troduced in the chlorophy11 estimated from uncorrected Rm(490)/R,(555)
ratios is lower (2.5%) than the one using ratios derived by corrections (20%) (Table 3.55). For other bludgreen RK ratios the corrections introduce noticeable improvement
(Table 3.5-2,Figure 3.5-7, and Figure 3.5-8).
The errors in L, computed from in-water measurements are estimated to be less
than 7% in blue and green portion of the spectmm. These errors are associated with
uncertainties in propagation of subsurface signal to the sea surface Le., by uncenainties in
determination of spectral attenuation coefficient k(A) by the algorithm proposed by Morel
(Equation 3.4-1). However. for typical observed chlorophyll concentrations of 1 mg m'3
and a measurement depth of 0.45 m, the possible uncertainty by factor of two in k(A)
would produce acceptable 5 7 % differences in computed L,(A,O-) and L,,..
Additional error
introduced by wave focusing effect on the upwelling signai was minimized by averaging
data over many wave periods.
[ nm]
412
Table3.5-1
Sunny
(Morecorrection)
(dter correction)
128.7
17.6
I
day: The
Root
Mean
3
Square Differences
(RMSD) of
uncorrected/corrected radiances for each waveband computed with respect to the waterleaving radiance estimated from in-water measurements.
- -
Rernote nnsing
reflectanw ratio
-
--
RMSD %
RMSD 96
(More correction) (rfter correction)
~
-
- -
-
# of datapoints
I
Table3.5-2
Sunny
day: The
Root
Mean
Square Differences
(RMSD) of
uncorrectedcorrected remote sensing reflectance ratios computed with respect to the
ratios estimated from in-water measurements.
wavelsrrgth
[ nm]
412
Table 3.53
RMSO 96
c o ~ o n ) ( after correction)
RMSD %
(bof-
# of datapoints
11.4
416.3
2
Overcast day: The Root Mean Square Differences (RMSD) of
uncorrected/corrected radiances for eacb waveband computed witb respect to the waterleaving radiance estimated from in-water measurements.
-
-
- -
-
Remote senring
reflectance ratio
RMSD %
(morecorradon)
RMSD %
(mercorrection)
# of datapoints
R4490) / Rn (555)
22.7
27.2
2
R, (443) / R m (555)
10.7
27.2
2
Ra (412) / R m (555)
3.12
39.2
2
Rrs (412) R m (443)
10.9
29.2
2
L
Table3.5-4
Overcast day: The Root Mean Square Differences (RMSD) of
uncorrected/corrected remote sensing nfiectance ratios computed with respect to the
ratios estimated from in-water measurements.
-
-
-
Corrected data
-
-
Bering Bara ampirical
algorithm
Bsting ma empirtcal
algorithm
I
Estimated trom From above
in-water
surîace
measurements measurements
1
sunny day
Relative
ditference %
1 RMSD =
0.8%
Chl relative
error %
Estimated
Ch1 [mglm7
1
RMSD = 2.5%
Derived by
corrections
Relative
difference O h
1
--
--
RMSO = 6.8%
RMSD = 27.2%
Tabk 3.5-5
1
.
No corrections
RMSO = 111.6%
Statistics for uncorrected and corrected data. The relative difference in R,,(490) I N,,(555) are calculated with respect to the
values estimated from in-water measurements. The chlorophyll concentration wüs computed using uncorrected/conected ratios. The
relative errors in chlorophyll are ohiained by propagating relative differences in H,,(41)0) I R,(w)
algorithm.
through the Bering sea enipirical
Figure 3.5-1 Before correction: Comparison of total radiance measured from airplane
LXabove-surface) to the water-leaving radiance estimated from in-water measurements
&(in-wurer). The wavebands are indicated by different symbols. Both sunny and overcast
days are included.
Figure 3.5-2 After correction: Comparison of w ater-leaving radiance L+,,,(correction)
retrieved by correction method from aircraft radiance. and &(in-warer) estimated from
in-water measurements. Measurements are performed at 7 wavebands which are indicated
by different symbols. Correlation coefficient is 0.99 and rmt mean square error is 0.03.
Both sunny and overcast days are included.
0.5
n
7
0.4-
O
L
cn
F
'€
c
O
0.3 -
V
O
7
E 0.2
-
3
=
-
O
0.1
*
O
0 .
e
m
1
a
Flight 1, sunny
Flight 2, sunny
Flight 3, sunny
Flight 4, overcast
Flight 5, overcast
a
-
O
- --- --
U
al
u
1
K
O
O
5 - - - - - - - & - - :
O
.-E -0.1
v
Y
3
A
A
-0.2
-
-
C
O
.-
g -0.3-
C
B
w
I -0.4
4
-
-0.5
400
4
1
1
1
450
500
550
600
wavelength [nm]
Figure 3.5-3 The deviations (bises. see Equation 2.5-7) of water-leaving radiances
derived by correction method L,&orrection) from &(in-water) estimated from in-water
measurements vs. wavelength. The fIights and the conditions during measurements are
indicated by different syrnbols. The dashed line indicates the best fit linear regression
through the points. The correction method tends to overestimate L, in blue part of the
spectrum and underestimate the green wavebands.
O
O
V
O
t
Flight 1, sunny
Flight 2, sunny
Flight 3, sunny
Flight 4, overcast
Flight 5, overcast
wavelength [nm]
Figure 3.54 After correction: Relative difference between water-leaving radiances
defi ved by correction method L(correction) and L(in-water) est imated from in-w ater
measurements vs. Wavelengh (Equation 2.5-8). The data from each measurement are
indicated by different symbols and connected with a solid line. The method tends to
overestimate L,,,. in blue part of spectrurn and underestirnate the green wavebands.
Benng sea. April23. sunny. Flight 1
1.2 *
I
I
f
I
I
./
CI
v
\
/
L
0.8
I
Lt (above-surface)
Lw (in-water)
Lw (correction)
1 -
03
I
\
-
-
U
0.2
-
- -*
a
*
400
450
500
550
600
650
700
750
800
wavelength [nm]
Figure 3.5-5 Sunny day: Example of sea-surface spectra recorded from aircraft,
L,(above-swface),spectral water-leaving radiance estimated from in-water measurements
&.(in-water),and spectral water-leaving radiance derived by correction method from L,,
L.(correction).The errorbars on
from Flight 1, Apri123, 1996.
L,represent the variance of mean spectra. The data are
Benng sea, April25, overcast, Fiight 5
I
r
1
I
1
I
i
Lt (above-surface)
Lw (in-water)
Lw (correction)
400
450
500
550
600
650
wavelengai [nm)
700
750
800
Figure 3.5-6 Overcast day: Example of sea-surface spectra recorded from aircraft,
L,(above-sutface),spectral water-leaving radiance estimated from in-water measurements
L ( i n- water),and spectral water-leaving radiance derived by correction method from Li.
LJcorrection). The errorbars on
from Flight 5 . April 25, 1996.
L, represent the variance of mean spectra. The data are
Bering Sea, sunny days
2,
1
8
1
Rrs ratio (in-water)
Figure 3.5-7 Sunny days before correction: Cornparison of remote sensing reflectance
ratios RdAl)l Rm(A2)calculated from total airborne radiance Rrs ratio(above-su@ace).to
the ratios calculated using water-leaving radiance estimated from in-water measurements
Rrs ratio(in-water).The ratios commonly used in pigment algorithms are indicated by
different symbols.
Bering Sea, sunny days
Rrs ratio (in-water)
Figure 3.5-8 Sunny days after comction: Cornparison of remote sensing reflectance
ratios Ru(&)/ R,(A2) calculated from comcted airborne data Rrs rario(correction) and
those estimated from in-water measurements Rrs ratio(in-water).The ratios commonly
used in pigment algorithms are indicated by different symbols.
Bering Sea, overcast days
I
I
I
Rrs(443) / Rrs(555)
Rrs(412) / Rrs(443)
Rrs(412) 1 Rrs(555)
-
A
w
O
F; 1.2 -
*
'i
a
8
O
1 -
-
0.8 -
-
(II
Y
O
r
E
d
-
O
O .5
1
Rrs ratio (in-water)
1.5
2
Figure 3.5-9 Overcast days before correction:Cornparison of remote sensing reflectance
ratios R,(AI)/ R,(Az) calculated from total airborne radiance Rrs ratio(above-sut$ace) to
the ratios calculated from water-leaving radiance estimated from in-w ater measurements
Rrs ratio(in-warer). The ratios commonly used in pigment algonthrns are indicated by
different symbols.
Bering Sea, overcast days
I
1
Rrs(490) 1 Rrs(555)
Rrs(443) 1 Rrs(555)
Rrs(412) / Rrs(443)
Rrs(412) / Urs(555)
d
4
Rrs ratio (in-water)
Figure 3.5-10 Overcast days after correction: Comparison of remote sensing reflectance
ratios RO(AI)/RJ&) calculated from comcted airbome data Rrs ratio(correction) and
those estimated from in-water measurernents Rrs ratio(in-water). The ratios commonly
used in pigment algorithms are indicated by different symbols.
Bering sea, Flight 5, overcast
wavelength [nm]
Figure 3.5-11 The spectral biases of L, retrieved by correction method, that would be
introduced by existence of water-leaving radiance in 780 nm band. The magnitude of
L,(780 nm) for which the biases are computed is indicated in the legend. The biases are
cornputed for signal typical for overcast conditions. The error in 780 nm band are
propagated through correction method to the rest of the spectrum. The existence of
L.(780nm) results in consistent underestimates of L.Particularly for low signals, small
biases c m represent large relative errors.
3.6.3 Overcast conditions
For the overcast day, the correction method gives an estimate of water-leaving
radiance in blue and green wavebands on average within 28%, and the L, values are in
general underestimated. The relative errors in L,are also wavelength dependen t (Figure
3.6-5), and bigger than the ones on sunny day (range to maximum 50%). As discussed in
previous section, wavelength dependent errors in L, introduce errors in remote sensing
reflectance ratios retrieval. For the overcast day, 1 found that al1 the uncorrected remote
sensing reflectance ratios show better agreement with in-water values than ratios denved
from corrected data (Table 3.5-4, Figure 3.5-9, and Figure 3.5-10). However, the error for
RU(490)/R,(555) ratio derived with no correction was still 22% which introduced
uncertainties of 9 1% in the chlorophyll estimate.
me error in R,(49O)/Rm(555) denved
from corrected data was 27.2% which propagated to chlorophyll gives 110% uncertainty
(Table 3 - 5 5 ) . That led to conclusion that for overcast day either corrected or uncorrected
aircraft data introduce uncertainties in the chlorophyll estimate by factor of two.
One of the uncertainties in correction of airborne data in overcast conditions arises
from Rayleigh scattering. The Rayleigh phase function is defined in tenns of the
scattering angle between the direction of incorning direct solar radiation and the direction
of light scattered into the remote sensing device (Equation 3.2-6). However, for overcast
conditions the direct source was not present, and the phase function computed using solar
zenith angle as an estimate of direction of incorning radiation does not properly describe
the angular distribution of scattered energy. On the other hand, if the Rayleigh scattering
is completely ignored, the results do not improve.
The major reason for relatively large uncertainties in retrieved quantities for
overcast day is connected with two problems: (a) whitecaps on the surface, and (b) very
low water-leaving radiance. For the measured wind speed of 10 ms-',the fraction of the
surface covered by whitecaps was estimated to be 1% (mode1 by Kwpke 1984). The
whitecaps can have a pronounced effect on the optical properties of the sea surface
(reflectance and transmittance), as well as on the optical properties of the ocean itself
(Mobley 1994. Zhang et al. 1998). The effect of whitecaps and foam on the radiance
observed by the airborne sensor is that the total signal consists of area-weighted averages
of the radiance leaving both the whitecaps-covered, and whitecaps-free areas. Since the
whitecaps reflectance is relatively high (22%, Koepke 1984) and nearly independent on
wavelength, the small amount of whitecaps alters the color of the sea surface (and surface
glint) toward white. That can explain the failure of the method to produce spectrally
correct surface glint corrections (Figure 3.54). However, the cornparison of results
estimated from above-water and from in-water measurements in the presence of
whitecaps becomes questionable, because L, estimated from in-water measurements is
associated with large uncertainties in the propagation of the subsurface signal across the
sea surface. On the other hand. the effect of whitecaps on the optical properties of the
ocean is due to the downward plume of bubbles injected by the breaking waves in the
upper few meters of the water. The bubbles enhance backscattenng over the whole visible
domain and consequently increase L,,.(780 nm) (Zhang et al. 1998). The actual existence
of L(780 nm) would lead to overestimates of the factor fi [ = M780)/ E,-&780)] and
surface glint, causing consistent underestimates of L,,. (as observed in the results).
Additionally,
L,for overcast day
was very small (-0.1 p W m" nm-' sr"). In order to
achieve 10% accuracy in L, the bias produced by the correction method should be within
0.01 pW m-' nm-' sr-'. This bias can be invoduced by a very small &.(780 nm) of 0.006
pW m*' nm" s i ' . There is a strong sensitivity of the method on the actual value of
&,*(780nm), when applied to low signals. The spectral b i s e s which would be introduced
by actual existence of L,,.(780 nm) are shown on Figure 3.5-1 1. Additional uncertainties
are introduced by the possible drifts of dark cumnts in the instrument which are
estimated to be about 4% of the measured low signal.
3.6 Conclusion
A method for atmospheric and surface glint c o d o n for low-flying (1 50-300 m)
aircraft ocean color data was presented. In the atmospheric correction, 1 included
Rayleigh scattering only and considered the atmospheric layer between the surface and
level of observation transparent. Outside of the direct sun-glint region the primary source
of glint is diffuse skylight reflected from the sea surface. For the sky-glint correction, the
method developed for shipbome data was applied, using estimated diffuse downwelling
irradiance. The method was tested on five flights, three under sunny conditions and two
under overcast skies.
For sunny conditions, the correction method performs well in retrieval of the
absolute value of water-leaving radiance. However. the Rn(490)/R,(555) ratios calculated
from uncorrected data agree better with the ones estimated from in-water measurements
then the ratios calculated frorn corrected data. The other bludgreen R, ratios computed
from corrected data for sunny conditions show noticeable irnprovement. The relatively
large uncertainties in retrieved quantities for overcast day were associated with whitecaps
and very srnail L.,
which was difficult to retrieve accurately with correction algorithm.
With regard to the operational use of aircraft ocean color data in chlorophyll
algorithms, proper correction would have to include measurements of diffuse sky
irradiance. If those measurements are not perforrned, the uncorrected data for sunny day
would give satisfactory chlorophyll estimates from R,(490)/R,(555)
ratios. If other
blue/green R, ratios are needed for bio-optical aigorithms, the corrections are necessary,
and modeled diffuse downwelling sky irradiance can be successfully used in correction of
airborne ocean color data 'collected under sunny conditions. For overcast day associated
with whitecaps, it was found that utilization of either uncorrected data or data corrected
by the proposed mehod would introduce uncertainties in the estimated chlorophyll by
factor of two.
These conclusions are derived on the bais of three flights in sunny conditions and
two under overcast sky. Because of lirnited number of datapoints they have to be taken
with cautious and need further validation.
Chapter 4
Summary
The main difficulty in correction of above-surface ocean color measurernents for
surface glint is to account for the reflection of variable sky, with randornly scattered
clouds, frorn a rough sea. This work represent an attempt to construct an operational
surface glint correction method for low-altitude remote sensing of ocean color that
applies for variable sky conditions. The method introduced sky irradiance as a key
variable that is used in the correction (instead of the more commonly used sky radiance).
If the diffuse radiance is not measured during experiment, the ratio of diffuse to global
irradiance c m be easily predicted for clear sky conditions frorn atmospheric models, and
used in correction.
In this work, both measured and modeled diffuse irradiances were used. In the
case of shipbome data, the results obtained by using measured diffuse irradiance were in
excellent agreement with surface tnith data, even under extremeiy variable sky
conditions. In the case of airborne data, after assessing the atmospheric correction, the
estimated diffuse sky irradiance was employed in surface glint correction. It was found
that under sunny conditions, the correction performed with acceptable accuracy. The
overcast conditions were associated with problems of whitecaps and the proper
evaluation of the method was not possible. However, the results demonstrate that the lowaltitude remote ocean color data collectai under clear or variable sky conditions can be
accurately corrected for surface glint using diffuse sky irradiance.
With regard to the operational use of the proposed surface glint correction
method, the future ocean color datasets should include rneasurements of diffuse sky
irradiance (for sky-glint correction), and high frequency measurements of sea surface
radiance (for sun-glint correction). The waveband in the red or near infrared portion of
the spectrum for which water-leaving radiance c m be assumed negligible should be
chosen adequately to the type of water under examination. Additionally, the whitecaps
should be avoided dunng remote sensing because they unpredictably change the optical
properties of the sea surface and the ocean itself.
The technical advantage of using diffuse sky inadiance for the correction is that it
can be measured with the same instrument as global downwelling irradiance: an upward
viewing radiometer where the diffise component can be determined by blocking the Sun
disc to the radiometer. This process c m be automated by using shadow-band radiometer
(Hamison et al. 1994). Thus. global and difise irradiance can be continuously monitored
during remote sensing rneasurements.
The cornparison of proposed method with other correction methods on the same
dataset was not possible, because the sky radiance was not rneasured during experiments
analyzed in this work. In order to resolve discrepancies between various methods for
surface glint correction, we collecteci an extensive high quality dataset of simultaneous inwater and above-water radiometric measurements (Venice, July 1998), which contains al1
the parameters necessary for cornparison. The future work will include exploration of this
extensive dataset and evaluation of uncertainties associated with various methods for
water-leaving radiance calculations cornmonly used in ocean color community.
Appendix A
Cox and Munk model for sun-glint
Cox and Munk (1954) in their analysis of photographs of the sun-glint pattern on
the wind-roughened sea surface deduced two important quantitative results:
the surface slope probability distribution, p. is function of wind speed v and follows a
Gaussian distribution:
where /? represents the angle between surface normal and vertical. and
d is the mean
square of the wave slope.
the mean square of the wave slope is linearly proportions! to the mean wind speed and
is given by:
a2= 0.003 + 0.005 12v
On the bases of these results. the BRDF of-the rough surface is expressed as:
(A-3)
where prw) is Fresnel reflectance for incident angle m. It is assumed that the incident sun
light is not polarized and dm)is given by:
and
sin o
a'= sin" n
The angles P and o are given in tenns of solar zenith angle 0, and angle of observation 8
p = cos-'
O>
coso - COS^,
2coso
(
= c..-'[r(i
1
1
1"'
+ cos y )
y = cos-' [cos O, cos8 + sin 8, sin 8 cos(<p - cp, )]
(A-@
where cp, and cp represent solar azimuth angle, and azimuth angle of the sensor
respectively.
This simple and effective mode1 is still widely used in ocean color community for
predicting the mean solar radiance reflected from rough sea surface.
References
Austin, R.W., "Inherent spectral radiance signatures of the ocean surface" In Ocean
color analysis, SI0 Ref. 74- 10, Scripps Institution of Oceanography, San Diego, 1974
Austin, R.W., 'The remote sensing of spectral radiance from below the ocean
surface", In Optical aspects of oceanography, ed. N. G. Jerlov & E. S. Nielsen, pp
3 17-344, Academic Press, London, 1974
Bartlett, J.S., The influence of Raman scattering by sea wuter and fluorescence by
phytoplanhn on ocean color, M.Sc. Thesis, Dahousie University, Halifax, 1996
Bird,R.E., Riordan, C., "Simple solar spectral model for direct and diffise irradiance
on horizontal and tilted planes at Earth's surface for cloudless atmospheres", J.
Climatol. Appl. Meteorol. Soc. 25: 87-97, 1986
Borstad, A., Brown, R.M.,Gower, J.F.R., "Airborne remote sensing of sea surface
chlorophyll and temperature dong the outer British Columbia coast", Proc. 61h
Canadian Symp. Rem. Sens., 54 1-9, 1980
Bukata, R.P., Jerome, J.H.,Bruton, J.E., "Particulate concentrations in lake St. Clair
as recorded by shipborne multispectral optical monitoring system", Remote Sens.
Envir., 25,20 1-229, 1988
Bukata, P.B.,Jerome. H.J., Kondrattyev, KY.,Pozdnyakov, D.V.,Optical properties
and remote sensing of inland and comtal waters, CRC Press, Boca Raton, 1995
Burt, W.V., "Albedo over wind roughened water", J-Meteorol. 1 1: 283-290, 1954
Carder, K.L., Steward. R.G., "A remote sensing reflectance model of a red tide
dinoflagellate off West Florida", LimnoL Oceunogr. JO,286298. 1985
10. Clarke, G.L.,Ewing, G.C.,Lorenzen, C.J.,"Spectra of backscattered light from the
sea obtained from aircraft as a measure of chlorophyll concentration", Science 167,
1 1 19, 1970
1 1. Cox, C, Munk, W., "Statistics of the sea surface derived from sun glitter", J. Marine
Res. 13, 198-277, 1954
12. Cox, C, Munk, W., "Measurement of the roughness of sea surface from photographs
of the sun's glitter", J. Opt. Soc. America 44, 838-850, 1954
13. Cox, C, Munk, W., 'Some problems in optical oceanography', J. Marine Res. 14, 6379, 1955
R.F., Johannesseen, S., Nieke, B., Parkhill, J.P.,
Stabeno, P.J., " Bio-optical variability in the Bering Sea as influenced by a mesoscale
eddy and shelf processes". EOS. Transactions, AGU Ocean Science Meeting, vol. 79,
No 1, 1998
14. Cullen, J.J., Ciotti, A.M., Davis,
15. Dickey, T.D., ''The emergence of concurrent high-resolution physical and bioopticd
measurements in the upper ocean and their applications", Reviews of Geophysics 29,
338-413, 1991
16. Gordon, H.R., "Removal of atmospheric effect from satellite imagery of the oceans",
Appl. Opt- 17, 163 1, 1978
17, Gordon, H.R., Clark, D.K., "Clear water radiances for atrnospheric correction of
costal zone color scanner imagery", Appl. Opt. 2û,4 175, 198 1
18. Gordon, H. R., Morel, A. Y., "Remote assessrnent of ocean color for interpretation of
satellite visible imagery, A review in Lecture notes on coastai and estaunne studies",
Ed. R.T. Barber, C.N.K- Mooers, M.J. Bowman, B. Zeitschel, Springer-Verlag, New
York, 1983
19. Gordon, H.R., Clark, D.K.,Brown, J. W., Brown, OB., Evans R.H., Broenkow,
W.W.. "Phytoplankton pigment concentration in the Middle Atlantic Bight:
cornparison of ship determination and CZCS estimates", Appl. Optics 22,20-36, 1983
20. Gordon, H.R., Brown, J.W., Evans, R.H.,"Exact Rayleigh scattering calculations for
use with the Nimbus-7 Coastal Zone Color Scanner", Appl. Opt. 37,862, 1988
21. Gordon, H.R., Brown, O.B., Evans, R.H.,Brown, J.W., Smith, R.C., Baker, K.S.,
Clark, D. K., "A semianalytic radiance model of ocean color", J. Geophys. Res. 93.
10909-10924, 1988
22. Gordon, H.R., Wang, M., "Surface roughness considerations for atmospheric
correction of ocean color sensors. 1: The Rayleigh-scattenng component", Appl. Opt.
31,4247, 1992
23. Gordon, J.L, Directional radiance (luminance) of the sea surface, Visibility
Laboratory, San Diego, S I 0 Ref. 69-20, SOpp, 1969
24. Gregg, W.W., Carder, K.L., "A simple spectral solar irradiance mode1 for cloudless
maritime atmospheres", Limnol. Ocecuiogr. 35, 1657-1675, 1990
25. Guzzi, R.. Riui, R., Zibordi, G., "Atmospheric correction of data measured by a
fiying platforni over the sea: eiements of a model and its experimental validation",
Appl. Opt. 26,3043-305 1, 1987
26. Guzzi, R., Maracci, G.C.,Rizzi, R., Siccardi, A., "Spectroradiometer for groundbased atmospheric measurements related to remote sensing in the visible from a
satellite", Appl. Opt., 24: 2859-2864, 1985
27. Harding, L.W., Itsweire, E.C., Esaias, W.E., "Determination of phytoplankton
chlorophyll concentrations in the Chesapeake Bay with aircraft remote sensing",
Remote Sens. Environ., 40,79- 100. 176.2 10, 1992
28. Harrison, L., Michalsky, J., Bemdt, J., "Automated multifilter rotating shadow-band
radiometer: an instrument for optical depth and radiation measurements", Appl. Opi.
33,51 18-5 125, 1994
29. Hanison, A.W., Coombes, C.A., "Angular distribution of clear sky shon wavelength
radiance", Soiar Energy, 40,5743,1988
30. Hoge, F.E., Swift, R.N., Yungel, J.K., "Active-pasive airborne ocean color
measurement. 2: Applications", AppL Opt. 25,48-57, 1986
R.N.,"Radiance ratio algorithm wavelengths for
remote oceanic chlorophy ll detemination", Appf. Opt. 26,2082-2093, 1987
3 1. Hoge, F.E., Wright, C.W.,Swift,
32. Iqbal, M., An introduction to solar radiation, Academic Press, New York, 1983
33.King, M., Bryne, D., Herman, B., Reagan, J., "Aerosol size distribution obtained by
inversion of spectral optical depth measurements", J. Amos. Sci., 35: 2 153-2 167,
1978
34. Kirk, J.T.O., Light and photosynthesis in aqucrtic ecosystems, Cambridge University
Press, Cambridge, 1994
35. Koepke, P., "Effective reflectance of oceanic whitecaps", AppL Op?. 23, 1816- 1824,
1984
36. Leckner, B., "The spectral. distribution of solar radiation at the earth's surfaceelernents of a model", Sol. Energy 20: 143- 150, 1978
37. Lee, Z.P., Carder, K.L., Steward, R.G., Peacock, T.G., Davis, C.O., Mueller, J.L.,
"Remote sensing refiectance and inherent optical properties of oceanic waters denved
from above-water measurements", Ocean Optics XIII, Proceeding SfIE, 160- 166,
1996
38. Maracci, G., Zibordi, G., "Atmosphcric optical thickness frorn ' 2 x radiometer' data*',
Int. J. Remote Sensing, 10: 1957- 1961, 1990
39. McArihur, L. J. B., Hay, J. E., "A technique for mapping the distribution of diffuse
solar radiation over the sky hemisphere", J. Appl. Meteorol. 20 (4), 42 1-429, 1981
40. Mobley, C. D., Light and Watec Radiative traRSfer in natural waters, Academic
Press, San Diego, 1994
'
4 1. Morel, A., "Optical modeling of the upper ocean in relation to its biogenous matter
content (Case 1 waters)",
Geophys. Res. 93, 1074%10768, 1988
42. Morel, A., Gentili, B., "Difise reflectance of oceanic waters.
aspects", Appl. Opt. 32,6864-6879, 1993
II Bidirectional
43. Morel, A., Voss, K.J.,GentililB., "Bidirectional reflectance of oçeanic waters: A
cornparison of modeled and measured upward radiance field, J. Geophys. Res. f 00,
13,143-13,150, 1995
44. Morel, A., "In-water and remote measurements of aiean color", Boundory-layer
MeteoroZ. 18,177-20 1, 1980
45. Mueller, J.L.,Austin, R.W., "Ocean optics protocol for SeaWiFS validation, revision
1 ", SeaWiFS Technical Report Series, NASA Technicai Memorandum 104566, Vol.
25, 1995
46. Neville, R.A., Gower, J.F.R., "Passive remote sensing of phytoplankton via ch1 a
fluorescence", J. Geophys. Res. 82,3487-93, 1977
47. O'Reilly, J.E., Maritorena, S., B.G. Mitchel, D.A. Siegel, K.L. Carder, S.A. Garver,
C.R. McClain, "Ocean color chlorophyl algorithms for SeaWiFS", J. GeopRes
unpublished, 1998
48. Paltridge, G.W., Plan, T., Radkitive proces in meteorology and climatology, Elsevier,
1976
49. Plass, G. N., Kattawar, G. W., Guinn, J. A., "Radiance distribution over a ruffled sea:
contributions from glitter, sky ,and ocean", Appl. Opt. 1 5 , 3161-3 165, 1976
50. Preisendorfer, R.W., Mobley, C.D.,"Albedos and glitter patterns of a wind-roughned
sea surface", J. Phys. Ocean. 16, 1293- 1316, 1986
51. Preisendorfer, R.W., Hydrologie optics, VoL4, Sutfaces, U.S.Dept. of Commerce,
NOAA, Environmental Research Laboratories, Pacific Marine Environmental
Laboratory, Honolulu, 1976
52. Raschke, E. "Berechnung des durch Mehrfachstreuung entstehenden Feldes solarer
Strahlung in einem System Ocean-Atmosphare", Bundesministerium fur Bildung und
Wissenschaft Forschungsbericht W 7 1-20, 1971
53. Saunders, P.M.,
"Radiance of the sea and sky in the IR window", J. Opt. Soc. Am., 58,
645-652, 1968
54. Shettle, E.P., Fenn, R.W., "Models for aerosols of the lower atmosphere and the
effect of the humidity variations on their optical properties" Air Force Geophysics
laboratory, Hanscomb AFB, MA 0 1731, AFGL-TR-79-02 14, 1979
55. Smith, R.C., Brown, O.B., Hoge, F.E.,Baker, K.S., Evans, R.H.,Swift, R.N.,Esaias,
W.E., "Multiplatform sampling (ship, aircraft, and satellite) of a Gulf Stream warm
core ring", Appl. Opt. 26,2069-2080, 1987
56. Smith, R.C., Baker, K.S., "Optical properties of the clearest natural waters", Appl.
Opt. 20, 177-84, 1981
57. Stxum, B.,'The atmosphenc correction of remotely sensed data and quantitative
determination of suspended matter in marine water surface layers", In Remore sensing
in meteorolgy, oceanography and hydrology, Ed A.P. CrackneIl, pp 163- 197, El l is
Horwood Limited, 1981
58. Sydor, M., "Remote sensing technique for accurate determination of volume
absorption coefficient of turbid water", unpublished, 1998
59. Takashima, T., "Polarization effect on radiative transfer in planetary composite
atmospheres with interacting interface", Earth Moon Planer 33, 59-97, 1985
60. Van Stokkom, H. T. C., Guui, R., "Atrnospheric spectral attenuation of airborne
remote-sensing data: Cornparison between experimental and theoretical approach",
Int. J. Remote Sensing 5,925-938, 1984
6 1. Wdker, R. E., Marine lightfield statistics, John Willey & Sons Inc., New York, 1994
62. Winter, B., Lighr scattering by a sea salt aerosol layer, M S c . Thesis, Dalhousie
University, Halifax, 1994
63. Wong, J., "Radiative forcing of sulfate aerosols", Unpublished, Dalhousie University,
Halifax, personal communication, 1996
The influence of phytoplankton pigments on the color of the seawater.
Deep-Sea Res. 7 , 1 , 1960
64. Yentsch, C.S.,
65. Zhang, X., Lewis, M., Johnson, B., "The influence of bubbles o n scattering of Iight in
the ocean", Appl. Op? 37,6525-6536, 1998
66. Zibordi, G., Maracci, G., Schlittenhardt, "Ocean colour analysis i;i coastal waters by
airborne sensors", Int. J. Remote Sensing 11,705-725, 1990
67. Zibordi, G., Maracci, G., "Determination of atmospheric turbidity from remotelysensed data", Int. J. Remote Sensing 9, 188 1- 1894, 1988
68. Zibordi, G., Parmiggiani, F., Alberotanza, L., "Application of aircraft multispectral
scanner data to algae mapping over the Venice lagoon", Remote. Sens. Environ. 34,
49-54, 1990