A AA 
lin = Is + la + Iref . (1) 
Here, Is is the spectral radiance from a terrain object with absorption 
by atmosphere. Let Ts be the surface temperature, 
  
: equati 
Is » T(1)-€s(1)-BO,Ts) , (2) Thus 
where T(A) is the atmospheric transmittance, €s(\) the surface emissivity, and 
B the Planck function. 
Ia is the upward spectral radiance of the atmosphere after emission and 
absorption by the succesive layers of atmosphere: where 
(i=1,2 
Ia = €a(4)- BO,Ta) , (3) 
where €a(A) is the atmospheric emissivity, and Ta the effective temperature of 
the atmosphere. 
In the lower atmosphere, local thermal equilibrium can be assumed, and 
Kirchhoff's law 
€a(A) = dal) (4) 
follows, where da(\) is the atmospheric absorptance. If T(\) includes the where 
extinction by the atmospheric scattering, OGa(A) is represented by 
Qa(À) 71-1). (5) 
With equations (3), (4), and (5), it follows that 
W(A1,T 
las(1- tO))-BG;Ta3) . : (6) 
Iref is the downward atmospheric spectral radiance, reflected upward at 
the surface of a terrain object, and attenuated through the optical path to 
the sensor. If the terrain object is sea surface, 
es(à) = 1 ; (7) 
can be assumed in thermal infrared region. Therefore the reflectance 
(1-es(X))=0, and the term Iref is negligiblé. 
Let T' be the apparent temperature determined by 
BOY, TY) in". (8) 
Then a simple form of the radiative transfer equation | 
lI rep 
W(A,T') = T(A)-W(A,Ts) + (1 - T(0))-WO,Ta) (9) to the 
When T. 
can be derived from equations (1),(2),(6),(7),and (8), using the relation in the 
Ag obtain 
[vB , Ta! algori 
W(A,T) = TE ’ (10) 
f: von»a' 
A1 
where U(A') is the spectral sensitivity of the total optical system in the 
spectral band [11,22], and A representing the band. 
bands 
functi 
320