500 
OSKAR ESSENWANGER 
400 
300 
Frequency ——e 
Ss 
"A ok” No 
002 00 O 
Logarithmic Scale 
25 063 158 
aah we 
398 10 257 631 
1 
006 016 040 100 251 631 68 398 wou™™ 
Fie. 3—Frequency distribution of daily precipitation amount at Munich 
in December—February 1880-1950, logarithmic scale 
In some instances, where the small amounts 
are unimportant or negligible, we may be satis- 
fied with such an approach. For a physical in- 
terpretation usually we have to deal with both 
great and small amounts. 
The transformation for physical reasons is 
based on the physical law involved in the proc- 
ess. Therefore, it is not based on the good fit for 
a part of the material but includes everything 
from a general point of view. 
The logarithmic scale—Now return to the 
treatment of precipitation data of shorter time 
intervals. For these, the author suggests the use 
of a logarithmic seale which has been applied in 
hydrology for a long time. Wischmeier and Smith 
[1958] established a logarithmic law for the ki- 
netic energy of rainfall. Schneider-Carius [1954] 
classified the rainfall process as autochthonous 
and also came to the conclusion that a logarith- 
mic law may dominate the rainfall process. The 
writer [Hssenwanger, 1956b] discussed some 
other facts pointing to a logarithmic law. 
The theory for the log-normal distribution by 
Chow [1954] and others indicate that any log- 
arithmie scale is suitable. Schneider-Carius [1955] 
and the author [EHssenwanger, 1959] have pub- 
lished some proposed scales which proved to be 
convenient for meteorological data. The daily 
data for Munich, December through February, 
previously shown in a cubic scale (Fig. 2) are 
now arranged in a logarithmic scale (Fig. 3). 
First we consider the total frequency only. The 
graph shows a mode at 2.51 mm. The frequency 
for the small amount is left open. This incom- 
plete part on the dry side is justified. Grunow 
[1956] has studied this problem thoroughly at 
Observatory Hohenpeissenberg. To summarize 
his result, a large percentage of the dry days 
may be reclassified as days with rainfall by eare- 
ful consideration of the precipitation amount, 
either not recorded or given under ‘traces.’ 
Therefore, rainfall records of shorter time pe- 
riods such as daily amount and less are truncated 
on the dry side, which almost eliminates any 
type of formal mathematical transformation. 
The detailed analysis of the data in Figure 3 
renders three partial collectives, each one a nor- 
mal distribution in a logarithmic scale. Under 
collective the author understands the definition 
used in many statistical books, a random sample 
for homogeneous conditions of the same physi- 
cal process. They are also submitted with Fig- 
ure 3, while a detailed discussion of the process 
and problem is given below. 
Frequency distributions and their analysis— 
In many cases meteorological events are defined 
