Prediction of Rainfall in Hawaii —Wentworth 
with useful accuracy. For this reason it was 
decided to examine the Honolulu Rainfall 
Index by a similar method for a further 
check (see Table 1). 
TABLE 1 
The Honolulu Intake Rainfall Index^ 
YEAR 
DECADES 
IN 
DECADE 
1890 
1900 
1910 
1920 
1930 
1940 
0 
132 
92 
122 
82 
108 
70 
1 
85 
101 
134 
108 
94 
79 
2 
91 
137 
85 
91 
117 
109 
3 
91 
110 
102 
124 
79 
91 
4 
100 
113 
100 
81 
94 
74 
5 
100 
107 
106 
81 
94 
64 
6 
66 
98 
134 
60 
109 
86 
7 
61 
123 
109 
154 
116 
8 
117 
88 
115 
83 
103 
9 
81 
95 
70 
87 
117 
* This index is now called the "intake” index, to distin¬ 
guish it from a "residential” index used for correlation 
with domestic consumption on lawn irrigation and the like. 
This index is the average of the per¬ 
centages of the mean for 10 stations in the 
intake area of the Honolulu water supply. 
It is much more representative of the rain¬ 
fall which provides water supply than is the 
record of the official U. S. Weather Bureau 
station, located in coastal Honolulu in the 
low rainfall belt. 
Our purpose here is to determine whether 
the values of the Honolulu index, taken on 
an annual basis, show systematic cycles in 
such a way that the rainfall of even 1 or 2 
years in advance can be predicted wifh useful 
validity. No attempt has been made here 
to correlate cycles of annual rainfall with 
any other natural cycles. Obviously, no value 
can be attached to any method of prediction 
unless it follows a definite routine which 
can be carried through uniformly by any two 
persons who follow the adopted rule. 
The first operation, similar to that used by 
Johnson, and others previously, is to calcu¬ 
late the mean differences between annual 
rainfall indexes separated by each of the 
intervals considered as a possible cycle. For 
217 
example, the differences between the indexes 
of the pairs 1890 and 1895, 1891 and 1896, 
1892 and 1897, carried through to 1940 and 
1945, are computed and averaged, without 
regard to sign. This value represents the 
average and also the most probable amount 
by which the rainfall of any given year will 
differ from one 5 years in the past or 5 years 
in the future. The same calculations were 
made for a 4-year interval, for 6 years, and 
so on, up to 20 years, with results shown in 
Table 2. 
The 4-year difference is the mean of 52 
values and that for 20 years is the mean of 
36 values. It is evident that the means have 
only a moderate range, that for a 16-year 
interval being the lowest, 20.8 per cent. 
Moreover, there is no marked superiority of 
this interval over the next, and so on. Thus 
the cyclical character is not strong. 
In order to estimate how much of the 
variation in annual rainfall is periodic, we 
first need a measure for random variation. 
Taking the whole series of 56 years, we find 
the standard deviation to be 20.3 per cent. 
TABLE 2 
Mean Variations in the Honolulu Rainfall 
Index for Cycles from 4 Years to 20 Years 
LENGTH OF 
CYCLE 
MEAN 
DIFFERENCE 
FOR YEARS 
ONE INTERVAL 
apart 
RANK, 
LOWEST TO 
HIGHEST 
Interval 
Per cent 
4 
22.4 
6.0 
5 
21.6 
3.5 
6 
24.3 
12.0 
7 
22.5 
7.5 
8 
24.0 
10.5 
9 
21.8 
5.0 
10 
26.5 
16.0 
11 
24.9 
13.0 
12 
21.6 
3.5 
13 
24.0 
10.5 
14 
22.5 
7.5 
15 
25.0 
14.0 
16 
20.8 
1.0 
17 
25.9 
15.0 
18 
28.2 
17.0 
19 
23.7 
9.0 
20 
21.2 
2.0 
