750
W-rrVg;
iri.
gP
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