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Proceedings of Symposium on Remote Sensing and Photo Interpretation

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
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 ...
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 . .
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-