505

RESULTS

its

Application of the above method gives reasonable approximation to the shape

of the haze size distribution function with some reservations to be discussed later

e

PHX

However, it was observed that some over compensation for high values in the small

radii size classes appeared as negative values in the larger sizes. This problem

was remedied by observing that no change in the law of scattering for a haze is

i .008

: -.005

-.021

: -.01

> -.006

made by multiplying the size distribution by a scalar. This observation follows

from the definition of the extinction coefficient and the phase function (Van de

Hulst, 1957). Thus the differences between the solution obtained and the "true"

solution should be no more than a constant factor.

All values of the solution which were negative were set to zero and extinction

coefficients were computed using this "trial” solution. The mean of the ratios

) .009

of the observed extinction coefficients to those computed from the "trial" solution

was computed. That is,

o> 00 LO ^ H ^

o o o o o o

o o o o o o

1 1

, M 3 .(A.)

1 . „ obs K .

L ~ M . , 8(A.)

1 = 1 1

The "trial solution was again modified by multiplying by C, that is N(r) = CN t (r),

N t (r) being the "trial" solution.

Table 2 displays the results of this operation for the three sites. Table 1

gives a tabulation of the extinction coefficients computed from the site distri

butions. Estimates of the extinction coefficient for the three sites appear to

be best when the wavelenth is in the interval of the data wavelength values.

)

LO 4

LO 4

LO 3

L0 2

REFERENCES

Phillips, D. L.

1962: A Technique for the Numerical Solution of Certain Integral Equations

of the First Kind. J. Ass. Comp. Mach., 9, p. 84.

Twomey, S.

1963: On the Numerical Solution of the Fredholm Integral Equation of the

First Kind. J. Ass. Comp. Mach., 10, p. 97.

Van de Hulst, H. C.

1957: Light Scattering by Small Particles. Wiley and Sons Inc., New York.

10‘ 2

Yamamoto, G. and Tanaka, M.

1969: Determination of Aerosol Size Distribution from Spectral Attenuation

Measurements. Applied Optics, 8, p. 447.