RELATION OF INDEX PATTERNS TO FALLOUT PEAKS
467
where n=1, 2, 3,.... Because of the symmetry of the current, by
integration over any nL/4 wavelengths, the mean absolute value of the
slope is thus
dy| _ 4A
4A
a
dx
(5)
L
Also, by definition,
| = tan |a|
(6a)
|e = tan [a|
(6b)
or
Here |a| is defined to be the mean absolute value of the deviation from
a pure west wind (a = 6 —270°, where @is the instantaneous wind
direction). By substituting Eq. 6b into Eq. 5 and solving for ja|, one
obtains
_
4
la| = arc tan “
(7)
which is an expression for the mean absolute value of the deviation
from westerly flow for a sinusoidal current of arbitrary amplitude and
wavelength,
Now,
if
a cyclone index is defined in terms of the previously
specified conditions for zonal (C = 1.0) and meridional (C = 0.0) flow,
one may write
c=1-/21
90°
(0°< |a| = 90°)
(8)
If this derived index is to adequately describe the state of the
flow of any given current, the value of |@| calculated from the given
sinusoidal current must compare favorably with the theoretical value
obtained from Eq. 7. The calculated value of |[@| is obtained from
this given sinusoidal current by measuring |a| at particular points
along a discrete grid interval. This grid distance must necessarily
be
less than one-half wavelength so that a reliable sample can be
obtained. The theoretical value of
[a@| from the given sinusoidal
current is then compared with the measured value of [a| obtained from
the same ideal current. The comparison between the measured and