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3 TEMPERATURE RETRIEVAL ALGORITHMS 
Different algorithms have been proposed for retrieval 
of SST from infrared satellite data. These algorithms 
range from physical solutions of the equation of radi 
ative transfer to algorithms based completely upon 
statistical regression analysis. The absolute accura-. 
ies vary from approximately IK for the single band 
direct solution algorithm, to a few tenths of a Kelvin 
for the split window algorithms (Prabhakara et.al., 
1974 , McClain, 1980). 
Weinreb and Hill (1980) describe an algorithm apply 
ing single band thermal infrared data. From the gene 
ral equation of radiative transfer in an attenuating 
medium, the absolute surface temperature is derived 
after having corrected for the atmospheric influence. 
The atmospheric correction is calculated from atmosp-e 
eric temperature- and humidity profiles from radio 
sondes. This algorithm is implemented for operational 
use at Troms0: Telemetry Station. In the next section, 
the thery for infrared SST techniques will be discus 
sed in more deail. 
3.1 The equation of radiative transfer 
For a cloud-free atmosphere, infrared radiation emit 
ted from the sea surface can propagate relatively un 
attenuated through the atmosphere at wavelengths for 
which gaseous absorption is small. Among these wave 
lengths, called 'atmospheric windows', the windows 
present at 3.5-4.0 um and 10-12 um are of interest for 
this application. 
The major absorbing gas present in the atmosphere is 
water vapr. Depending upon the concentration, the 
transmission through the atmosphere can range from >90 
% for a dry polar atmosphere (Pedersen, 1982), until 
<30 % for a humid atmosphere ( 5.5 cm water)(Njoku et. 
al., 1986). 
The complete expression for the infrared radiation 
detected by an airborne sensor consists of the compo 
nents from the sea surface, the atmosphere, and from 
downward radiation reflected at the surface into the 
direction of the sensor (Njoku et.al., 1986). However, 
in the thermal infrared the reflected component contri 
butes <1 % to the total radiance (Maul, 1981). There 
fore, neglecting this component will not introduce any 
significant errors in retrieving SST's. 
Based upon the theory of Wark and Fleming (1966) and 
Weinreb and Hill (1980), a simplified form of the 
equation of radiative transfer can be derived. 
At a given wavelength, X, the equation of radiative 
transfer through a plane-parallell, non-scattering 
atmosphere in local thermodynamically equillibrium can 
be given from the following relation: 
d{R (X»6 ) }= {- R (X/ 6) +B (.A, T (z) )} k (A) p(z) sec (6 )dz (3.1) 
where R(X/0) = the spectral radiance at wavelength! 
in wieving direction 0 from the nadir 
absorption factor of the gas 
absorbing gas density 
Planck radiation at wavelength X and 
temperature T 
altitude at local nadir' 
temperature versus altitude. 
From different assumptions summarized in Pedersen 
(1982), equation 3.1 can be written on the following 
form: 
k (X) 
p(z) 
B(X,T) 
T(z) 
R (X/ 0) = e (.X/0)B (X,T(p 0 ) ) t (.X,p 0 ,0 ) + 
1 
J. B {( X, T (P) ) } dt (.X/ p, 0) 
t ( X, p 0 , 0) 
where 
e ( X, 0) 
P 
P 
t (,A,p, 0 ) 
surface emissivity 
atmospheric pressure 
surface pressure 
atmospheric transmittance 
(3.2) 
at wavelength X, pressure p, in the direction 0. 
Equation 3.2 expresses the spectral radiance at one 
wavelength!.. The sensor onboard the satellite detects 
the total radiance within a passband of finite width. 
The expression for the total,normalized satellite 
sensor passband radiance, R£, is given from equation 
3.2 weighted by the passband response function H(X): 
X 2 h 
R (,('!) = / R ( X, 0) H (X) d X/ / H (A) dA (3.3) 
h ¿I 
where H(A) = the passband relative response at wave 
length X 
X_ = the maximum and minimum passband wave- 
2,1 
lengths. 
3.2 Atmospheric transmittance theory 
To obtain the surface temperature, T s , from equations 
3.2 and 3.3 on an operational basis, the atmospheric 
corrections have to be made. From the absolute, 
atmospheric corrected radiance, inversion of Planck's 
radiation law will give the surface temperature if the 
emissivity is known. 
For sea applications it is usual to assume the sea 
surface as a black body. This implies that the emis 
sivity, e ( X,0), in equation 3.2 is equal 1.0. 
The next step is to calculate the atmospheric trans 
mittance, t(tX,p o ,0). This can be done from the system 
LOWTRAN 6 (Kneizys et.al., 1983). However, when the 
algorithm was implemented, the LOWTRAN system was not 
available at Troms0.,Instead a procedure based upon 
the theory of Weinreb and Hill (1980), Wark et.al. 
(1974), and Weinreb and Neuendorffer (1973) was deve 
loped . 
The fundamental idea of this procedure is that the 
total atmospheric transmittance is given as the pro 
duct of the transmittances for the individual absor 
bing atmospheric constituents water vapor, nitrogen 
and the uniformly mixed gases. 
The real, inhomogenous atmosphere is treated as a 
succession of a number of homogenous layers, in each of 
which the pressure, p, temperature, T, and the water 
mixing ratio, w, are constants. 
The total transmittance for the most important cons 
tituent, water vapor, can be treated as the product of 
spectral line- and two different continua transmittan 
ces. The spectral line transmittances are calculated 
from an approximation suggested by Weinreb and Neuen 
dorffer (1973) . This method assumes the transmittance 
as a known function of the amount■of absorbing médium, 
U, temperature, T, and the total pressure, p, for each 
of the n-homogenous layers the real atmosphere is sub 
divided into. 
The water continua transmittances are calculated 
according to theory discussed by Roberts et.al. (1976). 
The two different transmittances can be explained from 
collisions between water vapor molecules (sb), and 
collisions between water vapor and other atmospheric 
gas molecules (fb). From the theory of Roberts et.al. 
(1976) and Weinreb and Hill (1980), the continua trans 
mittances can be given from the following expressions: 
p 2 
t sb (X,P)'oc G 0 (X) sec (0) i pr exp (T 0 (T-296) *))dp (3.4.a) 
P 
tfb (X,P) « C 0 (X) sec (0) / pr dp (3.4.b) 
0 
where 
COO = absorption coefficients at wavelength Xl 
P = total atmospheric pressure 
0 = wieving angle from local nadir 
r = mass mixing ratio of water vapor (g/kg) 
t , = transmittance from top of atmosphere to 
sb, fb , 
a level of pressure P. 
The Nitrogen transmittance can be derived from an 
expression 
tance (Wei: 
V X,P) . 
where the : 
notation o 
ficients a 
The tran: 
is calcula 
in the LOW' 
chey et.al 
treated as 
McClatchey 
Knowing 
radiative 
transmitta: 
rature T i; 
t (X,P,T) 
3.3 Emittei 
From the 
expression 
derived (D. 
ten on the 
R(X d ) = B( 
The notatii 
quation 3. 
Planck rad 
,T (p) ) 
In equatio: 
the centre 
In numer 
the integr 
intervals 
H (A ) is gi 
—-N, wher 
passband. 
3.4 Tests i 
In testing 
ances were 
atmospheri' 
ed to corn 
applied ati 
data from : 
2 , the com; 
listed. Thi 
water) , an< 
approximat- 
fairly rep. 
Arctic. A1 
From the 
an fairly 
ted transm 
loped rout 
transmitta: 
Knowing 
ance given 
temperatur' 
radiation 
deal with ' 
angle for i 
the surfaci 
In figuri