)

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-