Reflectance of ocean white caps.pdf

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Effective reflectance of oceanic whitecaps
Peter Koepke
The effective reflectance of the foam on the ocean surface together with the fraction of the surface covered
with foam describes the optical influence of whitecaps in the solar spectral range. This effective reflectance
is found to be -22% in the visible spectral range and is presented as a function of wavelength for the solar
spectral range. With the fraction of the surface covered with foam, taken from the literature, the results
lead to a good agreement with satellite measured radiances and albedo values. The effective reflectance is
more than a factor of 2 lower than reflectance values used to date in remote sensing and radiation budget
studies. Consequently, the optical influence of whitecaps can be assumed to be much less important than
formerly supposed.
1.
Introduction
increases with the proportion of whitecaps. Conse-
quently, the variability of whitecaps gives rise to a
variation in the radiance and the radiant flux densities
at the bottom and the top of the atmosphere.'
taken into account, both for remote sensing and in ra-
diation budget (climate) studies. In remote sensing
measurements, where the actual optical influence of
So, the correct optical influence of whitecaps must be
In the solar spectral range the reflectance of the ocean
into account as the product of their percentage area and
a reflectance value between 0.5 and
1.0.1,4,12
These
rather high foam-reflectance values are in the right
foam on water surfaces with patches of all ages and
consequently very different reflectances.
The aim of this paper is to determine the effective
reflectance of whitecaps which allows one to use the
W(U) values from the literature to describe the optical
influence of whitecaps.
11.
Reflectance of Ocean Surface
order of magnitude for fresh, dense foam but not for real
uncertainty in the remotely sensed quantity.
2
-
4
In
climate studies the correct optical influence of white-
caps should be taken into account, since oceanic foam
has an effect on the albedo of the ocean, affecting the
solar heating of its upper boundary layer which may
result in an alteration of the water temperature and the
depth of the mixed layer.
5
Austin and Moran have characterized the reflection
properties of the ocean surface with foam by deter-
mining the fraction of the surface with reflectance
within a given interval (a histogram of the surface area
as a function of the surface reflectance).
whitecaps is not precisely known, there is an equivalent
In the solar spectral range the reflectance of an ocean
surface,
Roc,
is composed of three components: re-
flection at foam, specular reflection, and underlight:
R.c
=
Rfstt
+
(1
-
W) R. +
(1
-
Rftot) Ru.
(1)
they have analyzed too few cases to establish a quanti-
tative relationship between reflectance of the sea surface
Unfortunately
and wind speed.
speed
U. -
However, statistical data are available which give .the
fraction covered with foam,
W
as a function of wind
6 11
In computations of radiance or radiant
The first term in Eq. (1) givesthe reflectance of the total
number of foam patches and streaks,
Rf,tot.
It is the
product of the fraction covered with whitecaps and the
reflectance of the whitecaps. It is described in detail
in the next section.
The second term describes the specular reflectance
at the water surface without foam. This component can
be calculated for a flat surface with the Fresnel formula
and therefore depends on the angles of incidence and
reflection and on the refractive index of the water.
Small spectral variations of this refractive index in the
in an unimportant decrease of the
R
values in this
range. The slope of the waves of the usually rough
ocean reduces and broadens the glint,
14 15
an effect
which must be taken into account in
R,
e.g., with data
after Cox and Munk.
1
6
spectral range between 0.4 and 1.5 m (Ref. 13) result
flux over an ocean surface, whitecaps are usually taken
The author is with Universit~tMnchen, Meteorologisches
Institut,
D-8 Mnchen 2, Federal Republic of Germany.
Received 2 November 1983.
0003-6935/84/111816-09$02.00/0.
© 1984 Optical Society of America.
1816
APPLIED OPTICS/ Vol. 23, No. 11 / 1 June 1984
weighted by (1
-
W), the area not covered with white-
caps, since specular reflection is possible only at that
part of the surface.
The
R
value in Eq. (1) is
The third part describes the reflectance due to un-
derlight
R,.
Although the underlight is scattered at
water molecules and suspended material in the water,
flectance for white increases toward the horizon, and
little account is taken of the less dense wind-generated
2
foam streaks.
4
Each of the photos contains whitecaps
of different ages; it follows that in the published W( U)
it can be described as a reflectance.
1 7
To take into ac-
count the reduction of underlight due to whitecaps,
RU
in Eq. (1) is weighted by the factor in the parentheses.
This factor is based on the assumption that the reflec-
tance of whitecaps is the same for light coming from
above or below. The reflectance due to underlight can
be assumed to be isotropic
1 7 1 8
due to the multiple
values whitecaps of different ages are taken into ac-
count.
The fraction covered with whitecaps, however, not
only depends on the wind speed but also on the fetch
9
scattering processes inside the water and to the
spreading of the radiance field emerging upward
through the water surface. The
RU
values show strong
1
spectral behavior,
7
depending on the material in the
water.
In ocean water
RU
can be neglected at wave-
In turbid waters with high sediment
and on the factors altering the mean lifetime of the
whitecaps, such as water temperature
2 5
and thermal
11
stability of the lower atmosphere. Consequently, an
expression for W(U) only as a function of the wind
speed, in the form given by Eq. (2),
W
=
a-
U,
(2)
lengths longer than 0.7 ,umdue to the spectral absorp-
tion of the water.
load, however, underlight is possible even at wave-
17
lengths above 1.0 Mm. '
19
The contributions due to whitecaps and underlight
are of the same order of magnitude. As mentioned
above, they depend on the wavelength, on the water
quality, and on the foam coverage. If an angle-depen-
dent reflection function of the ocean surface is used to
calculate radiances, Eq. (1) is also valid, but instead of
has a large uncertainty; different authors or different
statistical methods give different results.
1 0 11
Never-
theless, due to the lack of appropriate additional data,
the user will usually take an expression like Eq. (2) to
determine the area covered with whitecaps. In this
paper, the optimal W(U) expression by Monahan and
O'Muircheartaigh,
11
3 52
W
=
2.95
10-6.
U
.
,
(3)
reflectances the angle-dependent reflection function
must be introduced. In this case, in directions outside
the sun glint where the specular reflected component
is low, the contribution due to the diffuse components
underlight and whitecaps becomes important.
Therefore their exact values must be used and the ef-
fective reflectance of the whitecaps is required.
Ill.
Reflectance of Whitecaps
is used, which is valid for water temperatures
higher
than 14°C.
The optical influence of all the individual whitecaps,
the total foam reflectance
Rfatot,
is obviously the sum of
the optical influence of the individual whitecaps. The
optical influence is given by the product of the area of
each individual whitecap with its corresponding re-
flectance. These individual data are not, in general,
available; as mentioned above, usually a fixed
RJ
value
between 0.5 and 1.0 independent of wavelength or a
The spectral reflectance of dense foam of clear water,
Rf,
is -55% in the visible part of the spectrum as mea-
sured by Whitlock et
al.
20
in laboratory conditions.
wavelength-dependent
Rf
after Whitlock et
al.
2 0
is
combined with W(U) to describe the optical influence
of whitecaps:
Rttot
=
W Rf.
(4)
The value of -55% is valid up to 0.8-Mtmwavelength;
toward longer wavelengths the reflectance decreases due
to absorption of liquid water. The reflectance has two
relative minima at 1.5 and 2 ,m and can be assumed to
be zero at 2.7 MAm.Calculations with a simple model for
a whitecap consisting of more than twenty-five uniform
bubble layers also give a reflectance value of -55% in
21
the spectral range below 1 Mm.
The angle-dependent reflection function of whitecaps
However, the area of an individual whitecap increases
with its age while its reflectance decreases. An example
of this well-known behavior is shown in the photos in
Fig. 1 taken at 1-sec intervals. The figures to the left
of the fields givethe age of the dominant whitecap with
an uncertainty of 0.5 sec.
has not yet been studied. Usually they are assumed to
be isotropic reflectorsl4
2 2 23
,
which is in agreement with
visual inspection.
The relative area covered with whitecaps,
W,
is de-
termined by different authors
6
-
11
as a function of the
Since whitecaps of different ages are taken into con-
sideration in the W values, the combination of W with
Rf
values valid for dense, fresh foam gives
Rf,tot
values
that are too high. Consequently, a lower effective re-
flectance Ref must be used [Eq. (5)]:
Rftot
=
W
Ref-
(5)
10-m elevation wind speed U. They use photos of the
measured.
8
ocean surface where the outline of the white area is
The
traced, more or less, and the area is
surface is divided into subregions that are deemed, in
the judgment of the investigators, to contain white
water, all other regions are consequently dark water.
5
However, the threshold reflectance value that the in-
vestigators used as their decision criteria for white is not
The available photos yield Ref values only in the
spectral range up to 0.8 m. But they can be used to
determine an efficiency factor
fef,
independent of
wavelength, which allows the combination of spectral
Rf
values, as measured by Whitlock et
al.,
2 0
with the W
values depending on wind speed:
Rf,tot(
)
=
W *
fef
Rf (X)
1 June 1984 / Vol. 23, No.
11
/ APPLIED OPTICS
(6)
1817
known. The white water must stand out against the
water without foam. Consequently the threshold re-
age in
seconds
0.5
4.5
1.5
5.5
Fig. 1. Examples of the variation of a whitecap at
1-sec intervals, beginning at an age of 0.5 sec with an
uncertainty of ±0.5 sec: wind speed, 7.5 m sec';
water temperature, 15.7
0
C; viewing elevation,
600;
distance to foam patch, 35 m.
2.5
3.5
7.5
IV.
Method
whitecaps as a function of time was determined from
several series of photos. They were made from the
upper deck (30-m height) of the research platform
"Nordsee" in the German Bight at 50'43'N and 710'E
between 22 Aug. and 21 Sept. 1978. The reason for
working on the platform was to obtain ground truth
measurements to calibrate the European satellite
26
Meteosat.
wind speed conditions.
tion of an approximate
The variation in the size and reflectance of individual
and a wide-angle lens with a focal length of 50 mm. The
photos were taken as a series of -10, at intervals of 1 sec
and facing away from the sun. The elevation angle of
the camera was varied between
450
and 60°, resulting
in a distance to the analyzed whitecaps of between 33
and 60 m.
An analysis was made of the lifetimes of thirteen in-
and of six individual foam streaks from winds between
14 and 15 m sec'. Each whitecap detected for the
first time in a series must have been formed the second
dividual whitecaps, resulting from winds of 8 m sec',
cloud coverage conditions and, unfortunately, also low
Only a few series of photo-
value of the effective reflec-
This was done mostly in summer in low
before, since it was not present in the preceding photo.
taken at 1-sec intervals. Due to a restriction of the
graphs were made, but the material allows determina-
tance.
Meteorological and oceanographic parameters, such
Consequently, its age is 0.5 sec with an uncertainty of
+0.5 sec, as is also true for all the following pictures
lengths of the series, not all the whitecaps could be fol-
vidual whitecap.
Figure 2 shows 10 sec of the lifetimes
as wind speed and direction, wave height and period,
and water and air temperature, were continuously re-
corded by the equipment on the platform. The wind
speed at the 10-m level was estimated from that mea-
sured at the 47-m level using the logarithmic law with
a roughness length of 0.15 mm.
2 7
The water tempera-
ture was between 15 and 160C.
The camera was a 6- X 6-cm
2
Hasselblad equipped
with a motor drive, a red filter to enhance the contrast,
1818
APPLIED OPTICS/ Vol. 23, No. 11 / 1 June 1984
lowed until they vanished.
Figure 1 shows an example of the lifetime of an indi-
of different foam streaks. The streaks are fairly stable
and only vary slightly in size and reflectance.
Since the
that all foam streak were seen for the first time at an age
of 3.5 sec.
lifetime of such foam streaks is longer than 10sec, nei-
ther their beginning nor their end can be seen. Due to
this lack of information, in the evaluation it is assumed
seconds
0.5
4.5
1.5
5.5
Fig. 2. Examples of the variation of an ocean sur-
face with foam streaks at 1-sec intervals: wind
0
speed, 14.5 m sec'1, water temperature, 15.7 C;
viewing elevation, 500; distance to the center of the
image, 50 m.
6.5
2.5
3.5
7.5
To determine the area covered by a particular
whitecap, a common method was used: The photos
were projected onto graph paper, the outline of the
white area was traced, and the area was measured.
maximum.
The
area of each whitecap was normalized to be one at its
So normalized values of the area of foam
as a function of its age, a(t), are the results presented
in Figs. 3 and 4. It can be seen that the area of the foam
count for the variability of the reflectance due to the
scope of the wave without foam. The camera trans-
mittance curve was not taken into account, since the
whitecap in each series was placed in a fixed position.
The maximum reflectance was taken to be 55% as
measured by Whitlock et
al.
2 0
and as calculated by
Stabeno and Monahan
2
l for the spectral region of the
film material. Since this value was used as the mean
value for the total area of the fresh, dense foam patches,
patches increases during their lifetime.
The reflectance of the whitecaps was analyzed from
the film density, similar to the method described by
Austin and Moran.
5
If the reflectance of two points in
the target can be established, the density curve can be
graduated. These two reflectance values are the
Fresnel reflectance of the nonwhite vicinity of the
whitecap and the maximum diffuse reflectance of the
dense, fresh whitecap. To analyze the reflectance of
foam streaks, it was assumed that small portions found
with density values comparable with that of dense
whitecaps really have the maximum reflectance of dense
whitecaps. Due to the wide variation of the reflectance
over the area of the foam patches
5
the film density was
it is also in agreement with the value found by Austin
and Moran.
5
It can be assumed that the slope of the film density
curve is stable for at least ten pictures. So this slope,
starting at density values of the reflectance of dark
water in the vicinity of the whitecap, was used to de-
termine the reflectance of the whitecap, r(t), in each
picture of the series. Figures 5 and 6 show the decrease
in the reflectance as the whitecaps age.
Over a large area of the ocean, as analyzed in the
W(U) determination, it can be assumed that the age
distribution of the whitecaps does not alter with time.
Consequently, the mean effective reflectance of all the
whitecaps in the area can be determined as the effective
measured at many positions, and mean values were
determined.
A mean value also was used as the density
of the film in the vicinity of the whitecap to try to ac-
reflectance of an average whitecap, taking into account
its total lifetime.
1 June 1984 / Vol. 23, No. 11 / APPLIED OPTICS
1819
1.0
The reduction of the effective reflectance of white-
caps due to the expansion of their area and the thinning
of the foam can be assumed to be independent of the
wavelength. The effective reflectance Refdetermined
0.4
0.2
in the visible (and valid only for this spectral range if not
written as a function of A) can be converted to other
spectral regions or wavelengths with an efficiency factor
fef, which is derived as the ratio of the effective reflec-
tance to the reflectance of dense foam:
Ref
Ref
R
Ref
0.55
(8)
0
2
4
6
5
ange
in second s
10
Fig. 3. Normalized area of whitecaps (foam patches) as a function
of their age. The thicker stripes give the mean values. Wind speed
between 7.5 and 8.5 m sec'; water temperature between 15 and
16'C. The curve is calculated from Eq. (10) with
=0.25
and~y= 1.
N
Consequently, this efficiency factor can be combined
with spectral reflectance values
Rf (X)
of fresh, dense
foam as measured by Whitlock
et al.
20:
Ref(X)
=
fef
Rf (),
(9)
resulting in spectral values of the effective reflec-
tance.
0-
60-
50-
1.0-
0.4/
C
0.2
0
C
a
0
2
6
8
12
14
us
age in
seconds
0
~~
.
Fig. 4. Normalized area of foam streaks as a function of their age.
The thicker stripes give the mean values. Wind speed between 14
and 15 m sec; water temperature between 15 and 16°C. The curve
is calculated from Eq. (10) with
a
= 0.4.
2
6
B
age in seconds
4
~
-
a
I
10
Fig. 5.
values.
Reflectance of whitecaps (foam patches) in the visible spectral
Maximum reflectance of fresh dense foam
Rf
=
55% after
Whitlock
et al.
2 0
Other data as in Fig. 3.
range as a function of their age. The thicker stripes give the mean
nored if they were decayed to a reflectance less than the
threshold reflectance for white, which occurs at an age
the effective reflectance will be used in Eq. (5) in com-
But in the W(U) determination, whitecaps were ig-
60-
50-
-.
1
40-
C
0i
U
C
r
of the average whitecap. It followsthat the integra-
tion to determine Refends at time r, since the values of
bination with W(U) values. The effective reflectance
can be evaluated with Eq. (7):
f
Ref
=
|
30-
4a
a(t) r(t) dt
*
(7)
a,
20-
a,
1
0-
a(t)
dt
In the numerical solution, the products a
(t) r(t)
of each
us
individual whitecap are calculated and the integral is
determined from the mean values of these products.
The integration is performed as a sum with steps of
dt
= 1 sec.
1820
APPLIED OPTICS/ Vol.
23,
No.
11 / 1 June 1984
v
z
I
l
w
.T
g
.
w
M
w
I-I
0
I I
-
2
4
6
age in seconds
Fig. 6.
8
10
12
14
Reflectance of foam streaks in the visible spectral range as
a function of their age. Other data as in Fig. 4.

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