466
MAHLMAN
In the
previous
section the
desirability
of testing the relation
between the formation of extratropical cyclones and surface radioactive
fallout by using atmospheric indexes was mentioned. It is imperative
that the type of index parameter employed provides an adequate de-
scription of the relative amount of cyclonic activity in the atmosphere.
Because these cyclonic disturbances strongly influence the direction of
the upper wind field, it appears feasible that the derived index param-
eter be determined by the deviation of the mean wind vector from
westerly flow. It also will be advantageous to restrict the index to a
nondimensional and normalized form. In conformance with this reStriction, a purely zonal westerly current will be arbitrarily defined to
possess an index of 1.0 and a purely meridional current will be defined
to be 0.0. (These index values are now in the same senseasthe high
and low index concepts derived from the original zonal index.)
To simplify the mathematical approach as much as possible, one
may assume a time-independent sinusoidal velocity current at a given
height which is everywhere tangent to the isobars and is superimposed
upon a plane earth. The normal distance, y, of a given wave from the
x-axis in such a system is then given by
_
_ 20x
y=A sin [—
(1)
where A is the amplitude of the wave and L is the wavelength. The
Slope of the current at any point in this system is thus
dy _27A
27x
kL OS
(2)
The mean value of a function 6(£) over the interval a,b is defined
to be
~
1
>
B-5na f Ble) de
(3)
By Eq. 3, the mean slope of the sinusoidal current over one-fourth of a
wavelength is given by
ay) _
1
ama
fltlia
(= ~ @L+L/4—nL) L f
or which reduces to
@-<
27x
cos [> dx
(4a)
°