788
l pa ■ “«■*")
(2)
where oc(A,A 0 ) is the aerosol path radiance ratio at
two wavelengths A. and A 0 .
Under these assumptions the water leaving radiance
can be calculated from
w
a(A,Ao)(L Ao - (L^ + L^)) (3)
Equation (1) is to be solved for L w . From this value
the subsurface radiance just below the water surface
L can be calculated with
^u x
t L
(4)
negligable. For TM bands 1 to 4 are selected, where
band 4 (760 to 900 nm) is choosen as reference band.
2.2 Radiometric performance
The signal to noise ratio is for TM worse than for
CZCS (see tables 1 and 2). Tassan (1986) advises to
cluster 4*4 pixels to obtain a comparable or even
lower noise than the CZCS values. The resolution
becomes 120 m, still a considerable advantage over the
CZCS resolution.
x /
T = exp (
where T X j
thickness,
ozone or t
For the 02
ozone trar
each wave]
following
ozone _ ,
t - t
'4 8 5
2.3 Observation angles
ozone
T
56 0
where n is the refractive index of water, t the bi
directional transmission for a windroughened water
surface and T the total tansmittance, see equation 9.
Sorensen (1976:76) takes n=1.343; Austin (1974:320)
takes n=1.341. t=l-p, where p is the Fresnel reflec
tivity of a plane water surface assumed to be con
stant (0.021) for zenith view angles smaller than 45°
(Sorensen 1976:76), Austin (1974:323) gives for view
angles between 0° and 10° p = 0,0211.
In what follows, the terms in equations (3) and (4)
will be solved for Landsat TM.
Another important difference between CZCS and TM is
that the CZCS sensor can be tilted. This possibility
does not exist for TM. The CZCS was the first sensor
developed for water surface observations. With the
tilting sensor sunglitter may be avoided. Care should
to be taken that no sunglitter occurs on a TM image.
The advantage is that TM is always nadir-looking,
which implies that equations taking in account oblique
observation angles in Sturm's atmospheric correction
will simplify for TM.
ozone „
T = t
6 6 0
ozone _
T = C
8 3 0
The Raylei
nadir-look
M , , ,
p U‘±) -
in which 6
2 DIFFERENCES BETWEEN NIMBUS-7 CZCS AND LANDSAT TM
2.1 Spectral bands
The characteristics of the spectral bands used by
Nimbus-7 CZCS and Landsat TM are given in tables 1
and 2. For CZCS the bandwidth is equal for each
spectral band. This is not the case for TM. Besides,
CZCS spectral bands are narrower. These differences
will become important when calculating the solar
extraterrestrial irradiation, and when comparing the
absolute radiances received by each satellite, since
the radiative properties of the observed target and
the atmosphere may show a more important difference
over the larger TM spectral bands.
Table 1. CZCS spectral bands (Nykjaer et al.,
1984:2).
spectral
band
number
frequency
range
(nm)
center
frequency
(nm)
band
width
(nm)
signal/
noise
ratio
1
433-453
443
20
158/1
2
510-530
520
20
200/1
3
540-560
550
20
176/1
4
660-680
670
20
118/1
Table 2. Landsat TM
1983; NASA, 1982:4)
spectral bands
(Salomonson et al
spectral
frequency
center band
signal/noise
band
range
frequency width
screen radiance
number
(nm)
(nm) (nm)
minium maximum
1
450-520
485
70
52/1
143/1
2
520-600
560
80
60/1
279/1
3
630-690
660
60
48/1
248/1
4
760-900
830
140
35/1
342/1
For CZCS, spectral band
as a reference band where
radiance of "clear water"
4 (660 to 680 nm) was taken
the upwelling subsurface
was supposed to be zero or
3 CALCULATION OF THE RAYLEIGH PATH RADIANCE AND SKY-
GLITTER
3.1 Rayleigh path radiance
In a water-atmosphere system the Rayleigh path
radiance can be seen in a first approximation as
consisting of direct sunlight scattered by air
molecules and by the water reflected sunlight,
scattered by air molecules, both into the satellite's
field of view.
The first contribution is given by equation (5)
t (1 ) _ „ozone air M ,, . , c .
L pR = E 0 T T p (<JO (5)
in which Eo is the extraterristrial solar spectral
irradiance, T ozone the ozone transmittance, T air the
Rayleigh optical thickness (see section 3.3) and p^
(i|>~) the Rayleigh phase function.
The second contribution is given by equation (6)
Lp R } = pE 0 T T air p M (lM (6)
where p is the Fresnel reflectivity and T the total
transmissivity.
The extraterrestrial solar spectral irradiance,
which is function of the Julian day D and the wave
length A, can be calculated from
— 2
E 0 (D,A) = E„ (A){1 + ecos 3 g(D-3)} (7)
where E 0 (X) is the yearly average solar extraterres
trial irradiance at wavelength A, e the earth's orbit
eccentricity (0.0167) and D the Julian day. The
following values for the solar extraterrestrial
irradiance are based on Neckel and Labs (1981:246-247)
and made under the assumption that the TM sensor
radiometric response curve follows a gaussian curve :
3.2 Skygli
The skygli
by equatio
HG
PE 0 T
The three
bined in e
l pr + l hg
where the
T tot _ T oz
The ozone
has to pas
3.3 Mie op
The visibi
introduced
the scatte
defined by
given in e
V
3.912
K^ÔT
in which K
height 0 m
Since
K (0) =
5 5 0
E (485) = 192 mW/(cm 2 .sr.ym)
E (560) = 183 mW/(cm 2 .sr.ym)
E (660) = 160 mW/(cm 2 ,sr.ym)
E (830) = 109 mW/(cm 2 .sr.ym)
The Rayleigh optical thickness at wavelength A can be
approximated by equation (8) (Linke, 1956)
T air (A) = 0.00879 A -4,09 (8)
where K550
coefficien
K aero (0)
height 0 m
One obtain
„aero
K 550
(0)
All transmittances can be calculated from their
corresponding optical thicknesses with
Equation (
(temperatu
were Kftt
5 5 0