20
R n
EI k
j
n
k
m j
¦¦
1
1 1
30
,
(3.2)
where R is the mean annual rainfall erosivity (MJ mm ha
−1
h
−1
year
−1
), n is the
number of years of data, m j is the number of erosive events in the j year, and EI 30 is
the rainfall erosivity index of a storm k. The event’s rainfall erosivity index EI 30 is
defined as follows:
EI
I
ev
r
m
r r
30
30
1
§
©
¨
·
¹
¸
¦
(3.3)
where e r is the unit rainfall energy (MJ ha
−1
), and v r is the rainfall depth (mm) during
a time period r. I 30 is the maximum rainfall intensity during a 30-min period of the
rainfall event (mm h
−1
).
e
i
r
r
ª ¬
º ¼
0 29 1 072
0 05
.
.
exp
.
(3.4)
where i r is the rainfall intensity during the period (mm h
−1
).
The information required to calculate the R factor using the proposed method is
usually difficult to obtain in many parts of the world. Therefore, various studies
have been conducted to derive regression equations for the derivation of the R factor. These simplified methods provide great convenience for studying the spatial and
temporal variabilities of rainfall erosivity. Renard and Freimund (1994) proposed
the following equations for estimating the R factor using annual precipitation or the
Modified Fournier Index (MFI) when there are no data on rainfall intensity for a
particular site:
R
P
P
mm
u
0 04830
850
1 61
.
,
.
where
(3.5)
R
P
P
mm
u
t
587 8 1 219
850
2
.
.
, where
(3.6)
where R is the rainfall erosivity factor (MJ mm ha
−1
h
−1
year
−1
), and P is the average
mean annual precipitation.
R
M FI
MFI
mm
0 7397
55
1 847
.
,
.
where
(3.7)
R
M FI
MFI
M FI
mm
t
95 77 6 081
0 4770
55
2
.
.
.
,where
(3.8)
where R is the rainfall erosivity (MJ mm ha
−1
h
−1
year
−1
). MFI is the Modified
Fournier Index given below (Arnoldus 1977; Arnoldus 1980):
MFI
p
P
i
i
¦
1
12
(3.9)
3 Data Sources and Methodology