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