Cycles in Rainfall and Validity in Prediction 
of Rainfall in Hawaii 
Chester K. Wentworth 1 
In the present paper it is proposed first 
to discuss a recent book titled Correlation of 
Cycles in Weather, Solar Activity, Geomag¬ 
netic Values, and Planetary Configurations 
(Johnson, 1946). This discussion is fol¬ 
lowed by an application of a method of 
analysis therein described to the 56-year 
series of rainfall data for the Honolulu in¬ 
take area known as the Honolulu Rainfall 
Index (Board of Water Supply, 1947: 180). 
The conclusion is reached that this method 
does not result in prediction of the rainfall 
for a future year with sufficient accuracy to 
be of practical utility. 
The treatment by Johnson represents an 
enormous amount of labor in computing 
and compiling data. It carries much food 
for thought and exemplifies methods that 
other investigators will find useful for ap¬ 
plication to specific problems. The present 
discussion deals chiefly with the question of 
whether the data presented show the capa¬ 
city of the method to predict future rainfall 
quantities with useful accuracy. Some atten¬ 
tion is given to the general method and the 
suggested correlations between various other 
physical phenomena, but the present writer 
does not claim competent knowledge in most 
of these fields. 
The method used by Johnson in the 
analysis of cycles, or periodicities, is that 
previously used by Dinsmore Alter and 
described by him in 1937 and in several 
other papers cited by Johnson. This pro¬ 
cedure is comparatively simple and has 
1 Geologist, Honolulu Board of Water Supply. 
Manuscript received March 25, 1947. 
doubtless been devised and used by various 
students having occasion to do such work. 
It consists essentially of a process of finding 
that constant interval between pairs of years 
such that the average difference in rainfall 
between the two members of a pair is a mini¬ 
mum. For any given interval, the average 
error or difference between the first year’s 
rainfall and the next year’s rainfall is called 
the A index, presumably meaning the 
"Alter index.” The interval that is found 
to give the lowest A index is the period that 
is assumed to give the most reliable estimate 
of future values. 
Johnson has carried the method much 
beyond this point by subjecting the A differ¬ 
ences based on any one period to similar 
analysis to find a second period, and so on to 
several periods of diminishing importance. 
He has also made some use of an index he 
calls the J index, which appears to be the 
mean cumulative departure, resulting from 
the fact that the true cycle is a fractional 
period. 
It is not difficult to detect a periodic qual¬ 
ity in data on rainfall and other natural 
phenomena. For any given span of data, the 
most suitable period found in a first analysis 
will inevitably result in some improvement 
of estimate over that based on the arithmetic 
mean of experience, as defined by the stand¬ 
ard deviation or probable error. Johnson 
says, in his introduction, that an analysis 
based on a 20-year period for the rainfall of 
the Kualapuu, Molokai, area gave "very 
close agreement, estimated roughly in prac¬ 
tical value as 88 %, if fulfilled in the future. 
215 
