Another interesting effect is the rejection of renected sunlight by the radiometer. 

 Spectral measurements have been made looking directly at the reflection of the sun from 

 a river surface, indicating that the reflected energy is large at wavelengths shorter than 

 about 5m , but that at longer wavelengths the reflected radiation contributed by the sun is 

 much less than that emitted by the water.8 



Sky errors can, therefore, be reasonably ignored in the derivation of the equation. 



The radiant power P arriving at the detector in the Infrared Thermometer is given 

 K„D-fP +fP +fP where P , P , and P _ are the radiant 



^y^'o -^ocean a atmos r refl ^^ ^ocean' atmos' refl 



flux received from the ocean, from the atmosphere, and by reflection, respectively; the 

 co-efficients f f , and f represent the fractional portion of each of these radiation sources 



o' a r 



which lies within the spectral passband of the Infrared Thermometer, i.e., 8m to 14m . 

 According to the Stefan-Boltzmann law, this may be re-written P - f^tr € t T^ + f^ 



o-'aT'^ + f o-rtT"* where o- is a constant, t is the trans missivity of the atmosphere, 

 a r r „ ■ ■ 



€ is the emissivity of the ocean, a is the absorptivity of the atmosphere, r is the reflectivity 



of the ocean surface, and T . T , and T are the absolute temperatures of the ocean, at- 



o 3. r 



mosphere, and "reflected" targets respectively. 



We can simplify the expression by making several approximations (which are all 

 valid in the practical case), namely: 



T = T 

 r a 



f =f =f 

 oar 



Thus V= 0- € t T ^ + (a + r t) 0- T ^. But r = 1 - * and a + t - 1. Therefore, 

 ' o a 



approximately, P'= e t T ^ + (i - t t) T 4. This is the "indicated" temperature and wfll 

 (J- o a 



be hereafter referred to as T^ : T^^ = P^. Thus, T^^ = et T^4 + (i - , t) T^l 



Re -arranging, 



4 4 4 



€ t T ^ = T^ - (1 - t t) T 

 o 1 a 



4 4 4 



-^o = ^I -('-''^\ 



ft 



^o °'jV-(l-'^\ 



et 



-32- 



