268 
the samples of 5 -day data would probably be 
equivalent to a smaller sample of independent 
data than would the monthly samples. 
Daily Data: For comparison purposes only, 
daily rainfall amounts were correlated with 
700-millibar heights for the months of Jan- 
uary and February from 1946 through 1952. 
Only each fifth day was used, giving 77 pairs 
of relatively independent data at each grid 
point. The only rainfall index used was that 
for Hilo. 
HILO (winter) 
One of the strongest relationships revealed 
in this study was that between winter-time 
monthly rainfall at Hilo and the 700-millibar 
height at 37°N-163°W, in which a correlation 
of nearly +0.7 was found (Fig. 1). An ob- 
jective formula based on this coefficient was 
found to give substantially better results on 
independent data (see tests) than did the es- 
timates which were made by conventional 
methods. The correlation coefficient is based 
on 108 pairs of data, and the temptation is 
strong to consider it highly significant and 
meaningful in spite of the fact that the 108 
values do not constitute a random sample 
and that an unknown reduction in degrees of 
freedom must be considered in view of the 
possible serial correlation in the data. Since 
the coefficient in question is merely the best 
from among many, it must be examined very 
critically before any significance at all can be 
attached to it. Chance alone, however, would 
not give a coefficient this high in random 
samples of 108 cases once in 10® times, and 
the correlation is undoubtedly significant in 
spite of serial correlation and its having been 
selected from among 32 others. 
Some evidence of seasonal change in this 
pattern can be seen in the series of charts 
shown in Figure 3. Here the winter half-year 
pattern of Figure 1 is broken down into sep- 
arate patterns for each of the months. As 
only 18 pairs of data go into each correlation 
coefficient shown in this series, the patterns 
would, by chance, be expected to vary from 
PACIFIC SCIENCE, Vol. VIII, July, 1954 
month to month; however, it is seen that in 
each case the correlation is quite high at 
37°N-163°W. 
A physical explanation for the position of 
this key point is not difficult to provide on 
the basis of orography, and, as orographic rain- 
fall is of predominant importance to Hilo, 
this explanation is likely to suffice. The 
mountains behind Hilo enclose it in an arc 
which curves gently through approximately 
60 degrees. Thus, trade winds ranging in 
direction from due east to NNE will be cap- 
tured and lifted rather than deflected around 
the mountain mass (see map. Fig. 2). It may 
be supposed, then, that Hilo rainfall will be 
quite responsive to the strength of the trade 
winds and that, providing the winds are 
trades, the precise direction is not particularly 
important. 
In Figure 1 the direction and gradient of 
the isopleths over Hilo confirm this strong 
relationship between trade winds and rainfall. 
The maximum correlation at 37°N-l63°W 
simply indicates the spot where pressure ano- 
malies are most closely related to flow ano- 
malies in the Hilo area. If low latitude data 
were available, it might be possible to find 
a center of high negative correlation to the 
SSW of Hilo. 
Since the "strength of the trade winds" is 
proposed as the physical mechanism between 
the pressure at 37°N-l63°W and rainfall at 
Hilo, it might be supposed that a more nearly 
direct measure of trade-wind strength would 
have a still higher correlation. It is possible 
to test the gradient directly by correlating the 
difference in height between two grid points 
with Hilo rainfall. Such a correlation using 
the grid points 25°N-145°W and 20°N- 
140°W gave a coefficient of only 0.38. The 
discrepancy between the strength of this "di- 
rect" correlation and the best coefficient from 
the correlation field is not easy to understand. 
It emphasizes once again the difficulty of 
intuitive selection of parameters, particularly 
when mean charts and long-range problems 
are involved. 
