from CZCS imagery that S(x, ) can in fact remain essentially constant 

 over scales of hundreds of km, even in atmospheres with strong 

 horizontal inhomogeneities. When the aerosol phase function is 

 approximately independent of wavelength, the single scattering approxima- 

 tion shows that S is related to the optical properties of the aerosol 

 through 



S(A,A ) = E (X,X o ) F (X)/F o (A o ) 



(10) 

 x exp[-T 0z (X)-t 0z (X o )] Cl/y+l/y : , 



where t 0z is the ozone optical thickness, y and y Q are, respectively, 

 the cosines of the viewing angle and the solar zenith angle, and ( x » x ) 

 is related to the aerosol optical thickness t_ and single scattering 



a 



albedo u through 

 o 3 



u (X) (X) 

 e(X,X) = ° [ > *' ' . (11) 



»o<V a< x o> 

 Thus, L (x) can be found from 



W 



L W (X)= t(x) _1 L t (x)-L r (x)-S(X,X Q ) 



« cMx n )-Mx ft )-t(X ft )L JXJ] • 



(12) 



t v o' r v o' v o' w v o ; 



If x„ is choosen such that 

 o 



L„<V=0 (13) 



or 



t(X )L {X) < one digital count, 



W 



Equation 12 can be solved directly; however, if such a X Q does not exist 

 (as for example in Case 1 waters with <C> >l-2 mg/m ) a further 

 relationship amoung the various L 's is required. Smith and Wilson 



W 



B-13 



