) 
503 - 
, the haze 
where e is an undetermined constant. 
e quadrature 
To minimize the expression on the right side of (5) is equivalent to mini 
mize the expression 
) 
Z(f. , - 2f. + f. n ) 2 , f = f =0 
^ l-l l 1+1' * o N+l 
ts are given 
e matrix. 
Incorporating the constraint on f implied by (6) we have, to be minimized 
Zff. _ - 2f. + f. _) 2 +y _ 1 Z e 2 (7) 
l-l l 1+1' ' . i ^ J 
1 1 J 
rm of the 
X)} into the 
ecomes 
where y is a Lagrange multiplier. 
Minimizing (7) with respect to the f^, we obtain an expression involving e 
A^e = -yHf (8) 
where is the transpose of A and H is a matrix of the form 
). 
1-2 1 0 ... 
-2 5-4 1 0 ... 
1-4 6-4 1 0 ... 
nd. 
0 1-4 6-4 1 0 ... 
and Twomey 
data to extract 
the equation 
Solving the pair of equations (4) and (8) for f, we have the matrix equation 
f = (A*A +yH)A t g. 
) 
Data Aquisition 
is the quadra 
The data for this study were reduced from photometer observations at two 
continental sites (White Sands, N.M., 12 August 1973 and Phoenix, Ariz., 6 Sept. 
1973) and one maritime site (Rosenberg, Texas, 8 August 1973). The out put of 
nt . . 
1 
the photometer was calibrated for total optical depth of the atmosphere. Optical 
depths were measured for each of six wavelength channels from 0.38 ym to 1.1 ym. 
Haze optical depths were extracted from the total optical depth by removing alge 
braically the Rayleigh optical depth, with the assumption that the contribution 
to Rayleigh optical depth corresponding to the height of the haze layer was negli 
tion, there- 
lution to satisfy 
gible, since no information on the height of the haze layer was known, 
) 
Table 1 gives values of haze optical depth taken from smoothed photometer 
observations. The values followed by an asterisk were used as elements of the 
input vector, g. 
that its mag-