# Evaluation of Annual Rainfall Erosivity Index Based on Daily, Monthly, and Annual Precipitation Data of Rainfall Station

Authors: Ming-Hsi Lee; Huan-Hsuan Lin
Journal: International Journal of Distributed Sensor Networks
 (2015)

---

## Abstract

The erosivity factor in the universal soil loss equation (USLE) provides an effective means of evaluating the erosivity power of rainfall.
The present study proposes three regression models for estimating the erosivity factor based on daily, monthly, and annual precipitation data
of rainfall station network, respectively. The validity of the proposed models is investigated using a dataset consisting of 16,560 storm events monitored
by 55 rainfall stations in southern Taiwan. The results show that, for 49 of the 55 stations, a strong positive
correlation(r2>0.5)
exists between the annual rainfall amount and the annual rainfall erosivity factor. In other words, the estimation model based on the annual precipitation
data provides a reliable means of predicting the long-term annual rainfall erosivity in southern Taiwan. Furthermore, the root mean square error (RMSE)
and mean absolute percentage error (MAPE) analysis results show that the estimation models based on annual and monthly precipitation data have a more
accurate prediction performance than that based on daily precipitation data.


---

## Body

## 1. Introduction

Water erosion is one of the most important worldwide environmental concerns, particularly in tropical and subtropical regions of the world such as Taiwan. One of the most important active agents of soil erosion is rain due to its potential for producing soil disaggregation and subsequent removal. The effects of raindrop impact and surface runoff on soil erosion are generally estimated using the universal soil loss equation (USLE) [1]; namely,(1)A=RKLSCP,where A is the rate of soil loss (ton ha−1 yr−1), R is the annual rainfall erosivity factor (MJ mm ha−1 h−1 yr−1), K is the soil erodibility factor (t ha yr ha−1 MJ−1 mm−1), L is the slope length factor, S is the slope steepness factor, C is the cover and management factor, and P is the supporting practices factor [2, 3]. Amongst these factors, the erosivity factor (R) is recognized as one of the most effective measures for describing the rainfall erosivity power on a regional scale [4, 5]. In both the original USLE model [1] and the revised-USLE (RUSLE) model [6], R is calculated as the product of the storm rainfall energy (E) and the maximum 30-min rainfall intensity (I30). However, Wischmeier and Smith [7] also defined R as the average of the annual summations of the EI30 values for all storm events yielding more than 12.7 mm of rainfall.The rainfall erosivity index,R, describes the erosive impact of rainfall and runoff on both the detachment and the entrainment of soil and is given as [1] (2)Rj=Ej×Ij30=∑i=1TieiPji×Ij30,where Ej is the kinetic energy (MJ/mm), Ij30 is the maximum 30-min rainfall intensity (mm/h), ei is the unitary kinetic energy (MJ/mm·ha),  Pji is the rainfall amount (mm), and Ti is the total rainfall duration. Note that the subscripts i and j denote the number of rainfall data instances and the number of rainfall events, respectively. Summing the rainfall erosivity index of all the rainfall events over one year, the annual rainfall erosivity index can be obtained as(3)Ry=∑j=1YRj,where Y is the number of rainfall events in the year. In addition, the unitary kinetic energy ei is deduced from the relationship between the raindrop diameter and the rainfall intensity as follows [8]:(4)Ei=0.119+0.0873logIiforIi<76mm/hr,0.283forIi≥76mm/hr.The rainfall erosivity index,R, has been widely tested and applied in many countries and regions around the world whose rainfall intensity is characterized mainly as moderate to high [9–15]. In computing the rainfall erosivity factor, the maximum 30-min rainfall intensities for the storm and heavy storm events are generally computed on the basis of hyetograph data or high-resolution rainfall data (pluviograph data). Generally speaking, pluviograph data for at least 20 yrs are required to compute the rainfall erosivity for a given study area using the (R) USLE formulation [2]. However, such large volumes of data are not available for all regions of the world. Furthermore, even if sufficient pluviograph data are available, computing the rainfall erosivity is a complicated and tedious task. To overcome this problem, various simplified models have been proposed for estimating the rainfall erosivity factor using more readily available precipitation data.Among such models, those based on annual precipitation data are particularly common since annual rainfall data are available in most regions of the world and tend to be fairly reliable. Furthermore, various studies have shown that a good correlation exists between the annual rainfall erosivity and the annual precipitation amount at many locations around the world [16, 17]. Accordingly, annual precipitation data have been used to obtain simple estimates of the rainfall erosivity in many countries [2, 11, 18–34].Several researchers have used both annual precipitation data and maximum daily and hourly precipitation data to estimate the rainfall erosivity factor in the Mediterranean region [35, 36]. However, the models used in these studies estimate the mean annual rainfall erosivity over several yrs rather than the rainfall erosivity in a particular yr. Many regression models based on variations in the observed rainfall erosivity or seasonal erosivity have been proposed for predicting the daily rainfall erosivity [15, 33, 37–44] or monthly rainfall erosivity [45, 46]. It has been shown that the use of daily or monthly rainfall records provides a better understanding of the rainfall erosivity of individual storms than annual precipitation data [34]. In constructing daily or monthly prediction models, it is necessary to compute the rainfall erosivity on a daily or monthly basis, respectively. However, calculating the daily and monthly rainfall erosivity is more challenging than computing that for a particular storm. For example, if it rains from May 31 to June 1, the observed rainfall erosivity for this storm has just one value. However, the corresponding data should be divided into two different values (i.e., daily or monthly segments) when constructing daily or monthly models. Thus, the annual sum of the reclassified rainfall erosivity is different from the observed value due to the use of different boundary conditions. Moreover, the daily or monthly rainfall parameters used in daily and monthly models, respectively, provide an inadequate description of the kinetic energy and rainfall intensity terms in the rainfall erosivity index [33, 47].Although annual regression models are a gross oversimplification of the observed variation in the rainfall erosivity and their estimated values are rough [33, 48], they nevertheless represent a viable alternative to detailed quantitative assessments in providing a long-term assessment of the annual mean rainfall erosivity using the USLE formulation [49]. Thus, as discussed above, numerous researchers have proposed methods for estimating the rainfall erosivity based on annual precipitation data and/or other rainfall parameters. However, such models require careful optimization and calibration for each specific location and include site-specific coefficients. The proposed study is to find out the suitable models among daily, monthly, and annual precipitation data.The present study proposes three regression models for estimating the rainfall erosivity and finding out the suitable models in southern Taiwan based on daily, monthly, and annual precipitation data of rainfall station network, respectively, even without 30-min rainfall data. The detailed goals of this study can be summarized as follows: (a) to construct new models for the large-scale estimation of the erosivity factor in southern Taiwan and (b) to analyze the spatial distribution of the daily, monthly, and annual rainfall erosivity in southern Taiwan.


## 2. Materials and Methods

### 2.1. Study Area

This study considered the regions of Kaohsiung City and Pingtung County in southern Taiwan. The two regions cover areas of 2961 km2 and 2784 km2, respectively, and contain a total of 55 rainfall stations (see Figure 1). Both regions commonly experience extreme rainfall events during the summer months. For example, in August 2009, Typhoon Morakot resulted in catastrophic damage that left 665 people dead, 34 others missing, and roughly US$ 4.4 billion in damages.Figure 1
Geographic locations of 55 rainfall stations in southern Taiwan.


### 2.2. Rainfall Data

Table1 summarizes the basic geographic and rainfall data of the 28 rainfall stations in Kaohsiung City and 27 rainfall stations in Pingtung County over the 10 yr period extending from 2002 to 2011. Traditionally, the high-resolution rainfall data recorded by each station in Table 1 are used to calculate the rainfall erosivity factor in accordance with (2)–(4) [7]. In the present study, the reliability of these data was evaluated using the 10-min rainfall data obtained for the corresponding period from the Central Weather Bureau (CWB) of Taiwan. In the present study, 16,560 storm events were selected from the 550 observed annual rainfall datasets presented in Table 1 (i.e., 55 stations × 10 yrs). The corresponding daily, monthly, and annual rainfall data were then used for analysis purposes and for constructing the estimation models.Table 1
Geographic and rainfall data (2002~2011) for 55 rainfall stations in southern Taiwan.
Number
Rainfall station
Latitude
Longitude
Reference period (yr)
Elevation  (m)
Storm events
Annual rainfall (mm)
1
ZuoYing
120°17′N
22°40′E
10
13
230
1602
2
FongSen
120°23′N
22°32′E
10
61
241
1616
3
SaYe
120°16′N
22°50′E
10
35
366
1736
4
GangShan
120°17′N
22°45′E
10
31
259
1617
5
GuTingKeng
120°24′N
22°53′E
10
87
259
1421
6
MuJha
120°27′N
22°58′E
10
94
224
2154
7
CiShan
120°29′N
22°52′E
10
63
421
1996
8
FongSyong
120°21′N
22°45′E
10
55
290
1772
9
Jiashian
120°35′N
23°04′E
10
60
232
2650
10
SiBu
120°26′N
22°43′E
10
30
255
1903
11
FongShan
120°21′N
22°38′E
10
27
377
1787
12
DaLiao
120°25′N
22°36′E
10
24
302
1723
13
YueMei
120°32′N
22°58′E
10
112
212
2271
14
MeiNong
120°31′N
22°53′E
10
46
307
2227
15
JiDong
120°33′N
22°50′E
10
95
314
2257
16
JhuZihJiao
120°20′N
22°48′E
10
51
310
1799
17
JianShan
120°22′N
22°48′E
10
270
313
1823
18
SinFa
120°39′N
23°03′E
10
470
256
3032
19
DaJin
120°38′N
22°53′E
10
190
427
2710
20
YuYouShan
120°42′N
23°00′E
10
1637
381
4070
21
GaoJhong
120°43′N
23°08′E
10
760
241
2785
22
FuSing
120°48′N
23°13′E
10
700
380
2377
23
SiaoGuanShan
120°48′N
23°09′E
10
1781
355
2995
24
SiNan
120°48′N
23°04′E
10
1792
274
3750
25
MeiShan
120°49′N
23°16′E
10
860
319
2589
26
NanTienChih
120°54′N
23°16′E
10
2700
291
3661
27
PaiYun
120°57′N
23°27′E
10
3340
238
2642
28
NanSi
120°53′N
23°26′E
10
1949
438
2672
29
ALi
120°44′N
22°44′E
10
1040
263
2733
30
MaJia
120°41′N
22°40′E
10
740
248
3491
31
LiGang
120°29′N
22°47′E
10
42
310
2016
32
PingTung
120°30′N
22°39′E
10
25
292
2124
33
SinWei
120°32′N
22°45′E
10
56
352
2222
34
LinLuo
120°33′N
22°39′E
10
54
234
2230
35
NaJhou
120°30′N
22°29′E
10
20
306
1597
36
ChaoJhou
120°32′N
22°32′E
10
12
354
1848
37
FangLiao
120°35′N
22°21′E
10
69
305
1376
38
MaoBiTou
120°44′N
21°55′E
10
49
342
1419
39
JyuCheng
120°44′N
22°04′E
10
54
320
1610
40
LaiYi
120°37′N
22°31′E
10
74
363
2448
41
ChiShan
120°36′N
22°35′E
10
48
284
2630
42
SanDiMan
120°38′N
22°42′E
10
59
245
2575
43
LongCyuan
120°36′N
22°40′E
10
61
333
2438
44
LiLi
120°37′N
22°25′E
10
91
228
1944
45
ChunMi
120°37′N
22°22′E
10
86
387
1677
46
FangShan
120°39′N
22°14′E
10
36
197
1627
47
FongGang
120°41′N
22°11′E
10
63
307
1534
48
ShangDeWun
120°42′N
22°45′E
10
820
395
1700
49
GuSia
120°38′N
22°46′E
10
140
395
2582
50
WeiLiaoShan
120°41′N
22°49′E
10
1018
229
3548
51
SyuHai
120°53′N
22°11′E
10
20
227
2022
52
MouDan
120°50′N
22°11′E
10
285
273
2118
53
MouDanChihShan
120°50′N
22°09′E
10
504
251
2268
54
DanMenShan
120°44′N
22°06′E
10
260
364
1457
55
ShouKa
120°51′N
22°14′E
10
489
244
2184
Total
550
16560


### 2.3. Validation of Models

The present study developed three regression models based on the daily, monthly, and annual rainfall data, respectively, for estimating the annual rainfall erosivity factor (R) in southern Taiwan. The estimated values of R were then compared with the observed erosivity factors calculated using (2)–(4) [7]. For each model, the differences between the estimated and observed values at each rainfall station were evaluated in terms of the root mean square error (RMSE) and mean absolute percentage error (MAPE) computed as mentioned by Lee and Heo [17] as follows: (5)RMSE=Robe-Rest2,MAPE=Robe-RestRobe×100%,where Robe denotes the observed rainfall erosivity factor and Rest is the estimated rainfall erosivity factor.In order to develop an accurate model for estimating the rainfall erosivity, it must first be determined whether or not a significant relationship exists between the rainfall parameters and the rainfall erosivity. In identifying appropriate parameters for predicting the annual rainfall erosivity, the present study considered four different rainfall parameters, namely, the event rainfall amount (Pj), the daily rainfall amount (Pd), the monthly rainfall amount (Pm), and the annual rainfall amount (Py). The correlation coefficients between these parameters and the rainfall erosivity were calculated for each of the 55 rainfall stations. In addition, the coefficient of variation (CV) of the observed annual rainfall erosivity and annual rainfall was also computed for each station in accordance with (6)CV=σu,where σ is the standard deviation and u is the mean value.Figure2 summarizes the methods to develop the regional erosivity models from daily, monthly, and annual precipitation data.Figure 2
Flowchart of calculation.


## 2.1. Study Area

This study considered the regions of Kaohsiung City and Pingtung County in southern Taiwan. The two regions cover areas of 2961 km2 and 2784 km2, respectively, and contain a total of 55 rainfall stations (see Figure 1). Both regions commonly experience extreme rainfall events during the summer months. For example, in August 2009, Typhoon Morakot resulted in catastrophic damage that left 665 people dead, 34 others missing, and roughly US$ 4.4 billion in damages.Figure 1
Geographic locations of 55 rainfall stations in southern Taiwan.


## 2.2. Rainfall Data

Table1 summarizes the basic geographic and rainfall data of the 28 rainfall stations in Kaohsiung City and 27 rainfall stations in Pingtung County over the 10 yr period extending from 2002 to 2011. Traditionally, the high-resolution rainfall data recorded by each station in Table 1 are used to calculate the rainfall erosivity factor in accordance with (2)–(4) [7]. In the present study, the reliability of these data was evaluated using the 10-min rainfall data obtained for the corresponding period from the Central Weather Bureau (CWB) of Taiwan. In the present study, 16,560 storm events were selected from the 550 observed annual rainfall datasets presented in Table 1 (i.e., 55 stations × 10 yrs). The corresponding daily, monthly, and annual rainfall data were then used for analysis purposes and for constructing the estimation models.Table 1
Geographic and rainfall data (2002~2011) for 55 rainfall stations in southern Taiwan.
Number
Rainfall station
Latitude
Longitude
Reference period (yr)
Elevation  (m)
Storm events
Annual rainfall (mm)
1
ZuoYing
120°17′N
22°40′E
10
13
230
1602
2
FongSen
120°23′N
22°32′E
10
61
241
1616
3
SaYe
120°16′N
22°50′E
10
35
366
1736
4
GangShan
120°17′N
22°45′E
10
31
259
1617
5
GuTingKeng
120°24′N
22°53′E
10
87
259
1421
6
MuJha
120°27′N
22°58′E
10
94
224
2154
7
CiShan
120°29′N
22°52′E
10
63
421
1996
8
FongSyong
120°21′N
22°45′E
10
55
290
1772
9
Jiashian
120°35′N
23°04′E
10
60
232
2650
10
SiBu
120°26′N
22°43′E
10
30
255
1903
11
FongShan
120°21′N
22°38′E
10
27
377
1787
12
DaLiao
120°25′N
22°36′E
10
24
302
1723
13
YueMei
120°32′N
22°58′E
10
112
212
2271
14
MeiNong
120°31′N
22°53′E
10
46
307
2227
15
JiDong
120°33′N
22°50′E
10
95
314
2257
16
JhuZihJiao
120°20′N
22°48′E
10
51
310
1799
17
JianShan
120°22′N
22°48′E
10
270
313
1823
18
SinFa
120°39′N
23°03′E
10
470
256
3032
19
DaJin
120°38′N
22°53′E
10
190
427
2710
20
YuYouShan
120°42′N
23°00′E
10
1637
381
4070
21
GaoJhong
120°43′N
23°08′E
10
760
241
2785
22
FuSing
120°48′N
23°13′E
10
700
380
2377
23
SiaoGuanShan
120°48′N
23°09′E
10
1781
355
2995
24
SiNan
120°48′N
23°04′E
10
1792
274
3750
25
MeiShan
120°49′N
23°16′E
10
860
319
2589
26
NanTienChih
120°54′N
23°16′E
10
2700
291
3661
27
PaiYun
120°57′N
23°27′E
10
3340
238
2642
28
NanSi
120°53′N
23°26′E
10
1949
438
2672
29
ALi
120°44′N
22°44′E
10
1040
263
2733
30
MaJia
120°41′N
22°40′E
10
740
248
3491
31
LiGang
120°29′N
22°47′E
10
42
310
2016
32
PingTung
120°30′N
22°39′E
10
25
292
2124
33
SinWei
120°32′N
22°45′E
10
56
352
2222
34
LinLuo
120°33′N
22°39′E
10
54
234
2230
35
NaJhou
120°30′N
22°29′E
10
20
306
1597
36
ChaoJhou
120°32′N
22°32′E
10
12
354
1848
37
FangLiao
120°35′N
22°21′E
10
69
305
1376
38
MaoBiTou
120°44′N
21°55′E
10
49
342
1419
39
JyuCheng
120°44′N
22°04′E
10
54
320
1610
40
LaiYi
120°37′N
22°31′E
10
74
363
2448
41
ChiShan
120°36′N
22°35′E
10
48
284
2630
42
SanDiMan
120°38′N
22°42′E
10
59
245
2575
43
LongCyuan
120°36′N
22°40′E
10
61
333
2438
44
LiLi
120°37′N
22°25′E
10
91
228
1944
45
ChunMi
120°37′N
22°22′E
10
86
387
1677
46
FangShan
120°39′N
22°14′E
10
36
197
1627
47
FongGang
120°41′N
22°11′E
10
63
307
1534
48
ShangDeWun
120°42′N
22°45′E
10
820
395
1700
49
GuSia
120°38′N
22°46′E
10
140
395
2582
50
WeiLiaoShan
120°41′N
22°49′E
10
1018
229
3548
51
SyuHai
120°53′N
22°11′E
10
20
227
2022
52
MouDan
120°50′N
22°11′E
10
285
273
2118
53
MouDanChihShan
120°50′N
22°09′E
10
504
251
2268
54
DanMenShan
120°44′N
22°06′E
10
260
364
1457
55
ShouKa
120°51′N
22°14′E
10
489
244
2184
Total
550
16560


## 2.3. Validation of Models

The present study developed three regression models based on the daily, monthly, and annual rainfall data, respectively, for estimating the annual rainfall erosivity factor (R) in southern Taiwan. The estimated values of R were then compared with the observed erosivity factors calculated using (2)–(4) [7]. For each model, the differences between the estimated and observed values at each rainfall station were evaluated in terms of the root mean square error (RMSE) and mean absolute percentage error (MAPE) computed as mentioned by Lee and Heo [17] as follows: (5)RMSE=Robe-Rest2,MAPE=Robe-RestRobe×100%,where Robe denotes the observed rainfall erosivity factor and Rest is the estimated rainfall erosivity factor.In order to develop an accurate model for estimating the rainfall erosivity, it must first be determined whether or not a significant relationship exists between the rainfall parameters and the rainfall erosivity. In identifying appropriate parameters for predicting the annual rainfall erosivity, the present study considered four different rainfall parameters, namely, the event rainfall amount (Pj), the daily rainfall amount (Pd), the monthly rainfall amount (Pm), and the annual rainfall amount (Py). The correlation coefficients between these parameters and the rainfall erosivity were calculated for each of the 55 rainfall stations. In addition, the coefficient of variation (CV) of the observed annual rainfall erosivity and annual rainfall was also computed for each station in accordance with (6)CV=σu,where σ is the standard deviation and u is the mean value.Figure2 summarizes the methods to develop the regional erosivity models from daily, monthly, and annual precipitation data.Figure 2
Flowchart of calculation.


## 3. Results and Discussion

### 3.1. Relationship between Rainfall Parameters and Rainfall Erosivity

Figures3(a)~3(d) show the relationships between the event rainfall amount and the event rainfall erosivity, the daily rainfall amount and the daily rainfall erosivity, the monthly rainfall amount and the monthly rainfall erosivity, and the annual rainfall amount and the annual rainfall erosivity, respectively. In general, the results show that the rainfall erosivity varies from one geographic location to another, even under the same annual rainfall conditions. Figure 3(a) is one scatter plot of rainfall (Pj) and rainfall erosivity (Rj) that shows a significant nonlinear relationship (Rj=0.73Pj1.54,r2=0.80) between the event rainfall amount (Pj) and the event rainfall erosivity (Rj). Similarly, Figure 3(b) shows a significant relationship (Rd=0.50Pd1.66,r2=0.82) between the daily rainfall amount (Pd) and the daily rainfall erosivity (Rd). Figures 3(c) and 3(d) show that the monthly rainfall amount (Pm) and monthly rainfall erosivity (Rm) and the annual rainfall amount (Py) and the annual rainfall erosivity (Ry) are also related; that is, Rm=0.60Pm1.49, r2=0.91, and Ry=2.74Py1.20, r2=0.73, respectively. In other words, irrespective of the time interval considered, a relationship exists between the rainfall amount and the rainfall erosivity. Comparing the four intervals, it is seen that the strongest correlation exists between the monthly rainfall amount and the monthly rainfall erosivity.Figure 3
Scatter plots of (a) rainfall event amount (Pj) and rainfall event erosivity (Rj), (b) daily rainfall amount (Pd) and daily rainfall erosivity (Rd), (c) monthly rainfall amount (Pm) and monthly rainfall erosivity (Rm), and (d) annual rainfall amount (Py) and annual rainfall erosivity (Ry).
(a)
(b)
(c)
(d)Table2 shows the mean, minimum, maximum, and CV values of the annual rainfall amount and annual rainfall erosivity at each of the 55 rainfall stations over the considered time period (2002~2011). From inspection, the average annual mean rainfall over the 55 stations is equal to 2237 mm. Moreover, the minimum annual rainfall of 491 mm was recorded at the SyuHai station in 2002, while the maximum annual rainfall of 6224 mm was recorded at the YuYouShan station in 2005. The annual mean rainfall erosivity over all 55 rainfall stations is equal to 31118 MJ mm ha−1 h−1 yr−1. In addition, the minimum rainfall erosivity of 2271 MJ mm ha−1 h−1 yr−1 was measured at the DanMenShan station in 2002, while the maximum rainfall erosivity of 142370 MJ mm ha−1 h−1 yr−1 was measured at the YuYouShan station in 2005.Table 2
Annual rainfall and annual rainfall erosivity data (2002~2011) for 55 rainfall stations in southern Taiwan.
Number
Rainfall station
Annual rainfall (mm)
Annual rainfall erosivity (MJ mm ha−1 h−1 yr−1)
Regression models
r
2
Max
Min
Mean
CV
Max
Min
Mean
CV
1
ZuoYing
2373
700
1602
0.35
33723
7937
22454
0.35
R
y = 33.47P0.88
0.62
2
FongSen
2253
889
1616
0.31
39689
7512
22072
0.43
R
y = 66.47P0.78
0.29
3
SaYe
2373
1306
1736
0.23
33723
16132
23135
0.26
R
y = 0.90P1.36
0.71
4
GangShan
2671
909
1617
0.38
46687
8273
20975
0.61
R
y = 2.23P1.25
0.74
5
GuTingKeng
2656
537
1421
0.49
38869
5033
17198
0.63
R
y = 1.65P1.26
0.95
6
MuJha
4461
1412
2154
0.43
59574
16691
23355
0.52
R
y = 1.17P1.31
0.93
7
CiShan
3057
1091
1996
0.35
40927
13247
24545
0.40
R
y = 15.17P0.97
0.73
8
FongSyong
2814
881
1772
0.34
41035
10802
25122
0.42
R
y = 9.42P1.05
0.64
9
Jiashian
4461
1506
2650
0.39
76637
15779
41555
0.53
R
y = 3.10P1.20
0.75
10
SiBu
2981
982
1903
0.34
49680
10644
27468
0.50
R
y = 0.59P1.42
0.86
11
FongShan
2672
867
1787
0.33
37336
11659
24753
0.38
R
y = 6.92P1.09
0.77
12
DaLiao
2454
821
1723
0.31
32686
7103
22962
0.38
R
y = 3.68P1.17
0.66
13
YueMei
3598
1410
2271
0.28
41677
17889
25374
0.33
R
y = 17.90P0.95
0.74
14
MeiNong
3399
1083
2227
0.35
59758
16033
31859
0.49
R
y = 5.62P1.12
0.81
15
JiDong
3221
1171
2257
0.30
47197
18988
32550
0.29
R
y = 684.83P0.50
0.30
16
JhuZihJiao
2848
876
1799
0.36
49183
7989
24302
0.55
R
y = 9.36P1.05
0.53
17
JianShan
3063
632
1823
0.39
60047
6044
26262
0.58
R
y = 1.27P1.32
0.86
18
SinFa
4589
1630
3032
0.34
75976
21836
47935
0.44
R
y = 4.47P1.15
0.76
19
DaJin
4105
1322
2710
0.32
66543
13987
40181
0.42
R
y = 0.95P1.34
0.83
20
YuYouShan
6224
1767
4070
0.34
142370
19412
72039
0.50
R
y = 0.43P1.44
0.88
21
GaoJhong
4565
1188
2785
0.40
69908
12387
40858
0.54
R
y = 1.28P1.30
0.72
22
FuSing
4231
1077
2377
0.46
81114
7355
33084
0.73
R
y = 0.81P1.35
0.65
23
SiaoGuanShan
4164
1697
2995
0.26
93739
14726
41586
0.54
R
y = 0.16P1.55
0.66
24
SiNan
5557
1800
3750
0.32
98956
13550
46899
0.59
R
y = 1.50P1.25
0.54
25
MeiShan
4270
1122
2589
0.39
69331
10799
33285
0.65
R
y = 0.25P1.49
0.77
26
NanTienChih
4986
1615
3661
0.33
101544
9538
41011
0.73
R
y = 0.02P1.74
0.73
27
PaiYun
3844
1294
2642
0.32
33848
6862
18175
0.48
R
y = 0.45P1.33
0.79
28
NanSi
3572
1230
2672
0.33
48871
6949
24998
0.56
R
y = 0.033P1.72
0.86
29
ALi
4049
1661
2733
0.34
59940
15606
35257
0.51
R
y = 0.35P1.45
0.86
30
MaJia
5530
1820
3491
0.35
122022
25807
64926
0.50
R
y = 6.25P1.12
0.64
31
LiGang
3142
1201
2016
0.32
39945
12491
27605
0.33
R
y = 23.31P0.93
0.62
32
PingTung
3351
990
2124
0.34
65988
10229
32927
0.50
R
y = 1.84P1.27
0.76
33
SinWei
3999
1312
2222
0.37
87155
13318
36733
0.60
R
y = 2.38P1.24
0.64
34
LinLuo
3267
1139
2230
0.30
53448
17799
32012
0.34
R
y = 51.92P0.83
0.61
35
NaJhou
2340
773
1597
0.33
33690
9998
20852
0.38
R
y = 43.40P0.83
0.54
36
ChaoJhou
2581
811
1848
0.32
52474
6426
27321
0.49
R
y = 0.97P1.35
0.66
37
FangLiao
2311
534
1376
0.47
28044
4763
16425
0.50
R
y = 8.67P1.03
0.81
38
MaoBiTou
2050
998
1419
0.21
99535
10631
22740
1.19
R
y = 0.002P2.19
0.49
39
JyuCheng
2218
986
1610
0.26
62730
7558
23929
0.70
R
y = 0.07P1.71
0.64
40
LaiYi
3439
1556
2448
0.24
82126
21753
43166
0.47
R
y = 10.17P1.06
0.36
41
ChiShan
3714
1347
2630
0.28
67586
15140
41204
0.38
R
y = 4.87P1.14
0.61
42
SanDiMan
3773
1655
2575
0.26
75709
20727
42442
0.44
R
y = 1.27P1.32
0.64
43
LongCyuan
3653
1249
2438
0.31
65942
12170
34742
0.44
R
y = 2.27P1.23
0.67
44
LiLi
2864
1137
1944
0.31
39750
12995
26451
0.38
R
y = 17.46P0.96
0.56
45
ChunMi
2615
847
1677
0.33
32659
7211
19299
0.45
R
y = 1.82P1.24
0.75
46
FangShan
2281
1074
1627
0.27
66431
8886
20485
0.81
R
y = 0.17P1.56
0.58
47
FongGang
1972
849
1534
0.27
37847
5489
17706
0.49
R
y = 0.77P1.36
0.68
48
ShangDeWun
2671
909
1700
0.33
42345
11248
54945
0.16
R
y = 17.34P0.99
0.59
49
GuSia
3495
1598
2582
0.27
48113
16361
35280
0.32
R
y = 2.78P1.20
0.73
50
WeiLiaoShan
5666
1377
3548
0.40
121787
14042
61679
0.52
R
y = 2.66P1.23
0.87
51
SyuHai
2939
491
2022
0.37
53235
4231
28585
0.49
R
y = 2.14P1.21
0.88
52
MouDan
2661
1396
2118
0.20
50943
13706
22589
0.50
R
y = 0.50P1.41
0.56
53
MouDanChihShan
3377
1577
2268
0.26
53046
13279
24154
0.52
R
y = 0.99P1.30
0.50
54
DanMenShan
2129
558
1457
0.41
30074
2271
16433
0.49
R
y = 10.52P
0.48
55
ShouKa
2606
1735
2184
0.16
28325
10158
24854
0.20
R
y = 1.24P1.25
0.52An inspection of Table2 shows that the correlation coefficients (r2) between the mean annual rainfall and the rainfall erosivity range from 0.29 to 0.95. Moreover, 49 of the 55 stations have a correlation coefficient (r2) greater than 0.5, which are satisfied by a significance test (two-tailed test) with a 99% confidence level (P value < 0.01). The CV values of the annual rainfall range from 0.16 to 0.49, while those of the annual rainfall erosivity range from 0.16 to 1.19. Of all the stations, the GuTingKeng station has the highest CV  (0.49) for the annual rainfall, while the MaoBiTou station has the highest CV  (1.19) for the annual rainfall erosivity.GIS (Geographic Information System) was used to interpolate and plot the spatial variability of the annual rainfall erosivity factor (Ry) over the study area using the Kriging interpolation method [16]. Figures 4(a) and 4(b) show the results obtained for the annual rainfall and annual erosivity, respectively. An inspection of Figure 4(a) shows that the mean annual total rainfall ranges from 1376 to 4070 mm yr−1. Based on the regression relationship for the annual rainfall (Ry=2.74Py1.20), the rainfall gradient values range from 14785 to 72039 MJ mm ha−1h−1yr−1. Moreover, the Kriging interpolation results show that the annual rainfall erosivity has a west-east gradient with values ranging from 15000 to 70000 MJ mm ha−1 h−1 yr−1. It is seen that the spatial distributions of the annual rainfall and annual rainfall erosivity, respectively, are similar. Different interpolation methods may result in different spatial distributions of the rainfall erosivity. However, Angulo-Martínez and Beguería [33] found that all common interpolation methods are capable of capturing the regional distribution of the R factor given the use of a spatially dense rainfall database with a high temporal resolution.Figure 4
(a) Annual precipitation and (b) annual rainfall erosivity maps in southern Taiwan. Note that isohyet and isoerodent intervals are 500 mm and 10000 MJ mm ha−1 h−1 yr−1, respectively.
(a)
(b)The rainfall erosivity map presented in Figure4(b) is of great relevance for soil erosion evaluation and control. It has implications not only for agriculture but also for many activities related to land use planning. Furthermore, it can be used as a guide for soil conservation practices and landscape modeling since the R factor is usually an important part of erosion models such as the USLE [16].The higher erosivity observed in the tropic region is caused by the high amount of precipitation, intensity, and kinetic energy of rain. The main generating mechanism of rainfall is convection effect in most tropical regions. As a result, the regions receive more rain with higher intensities than the temperate regions, dominated by midlatitude cyclones [41].The regression models to estimate rainfall erosivity for specific locations are unable to accurately predict actual rainfall erosivity for other locations due to site-specific conditions. Therefore, simplified methods based on annual precipitation for estimating rainfall erosivity should be used with caution according to location or time period. Their results deserve careful attention as applying simplified methods to estimating annual rainfall erosivity.


### 3.2. Applicability of Three Regression Models

The applicability of the daily, monthly, and annual regression models developed in the previous subsection (i.e.,Rd=0.50Pd1.66, Rm=0.60Pm1.49, and Ry=2.74Py1.20, resp.) was evaluated by comparing the results obtained from each model for the rainfall erosivity factor with the observed rainfall erosivity factor computed using the method presented by Wischmeier and Smith [7]. Table 3 presents the RMSE and MAPE analysis results for the estimated and observed rainfall erosivity values. It is seen that when estimating the Ry factor using (3) based on the daily rainfall data, the MAPE ranges from 2% to 49% (CV=0.50) and the RMSE varies from 1031 to 16350 MJ mm ha−1 h−1 yr−1 (CV=0.55). Similarly, when estimating the Ry factor using the monthly rainfall data, the MAPE ranges from 1% to 37% (CV=0.87), while the RMSE varies from 190 to 17345 MJ mm ha−1 h−1 yr−1 (CV=0.96). Finally, when estimating the Ry factor based on the annual rainfall data, the MAPE ranges from 2% to 30% (CV=0.59) and the RMSE varies from 454 to 16030 MJ mm ha−1h−1yr−1 (CV=0.85). Overall, it can be seen that the estimation errors of the three models range from 11% to 49%. For the daily model, the error rate exceeds 10% at 11 of the 55 stations. However, for the monthly and annual regression models, the error rate is less than 10% for 34 and 24 of the 55 stations, respectively.Table 3
Comparison of estimated rainfall erosivity factorRy and observed rainfall erosivity factor Ry (unit: MJ mm ha−1 h−1 yr−1).
Rainfall station
R
y
R
y
∗
R
y
∗
∗
R
y
∗
∗
∗
RMSE*
RMSE**
RMSE***
MAPE*
MAPE**
MAPE***
ZuoYing
22454
26889
18927
19208
4435
3527
3246
20
16
14
FongSen
22072
25814
16576
19409
3742
5496
2663
17
25
12
SaYe
23135
27360
20807
19680
4225
2328
3455
18
10
15
GangShan
20975
19239
18767
19412
1736
2208
1563
8
11
7
GuTingKeng
17198
25627
20154
16625
8429
2956
573
49
17
3
MuJha
23355
32082
22104
25164
8727
1251
1809
37
5
8
CiShan
24545
27016
26060
24999
2471
1515
454
10
6
2
FongSyong
25122
33138
22358
21677
8016
2764
3445
32
11
14
Jiashian
41555
50785
40394
35132
9230
1161
6423
22
3
15
SiBu
27468
37029
25515
23613
9561
1953
3855
35
7
14
FongShan
24753
30880
22707
21887
6127
2046
2866
25
8
12
DaLiao
22962
29446
21045
20955
6484
1917
2007
28
8
9
YueMei
25374
35168
31863
29181
9794
6489
3807
39
26
15
MeiNong
31859
43738
30787
28519
11879
1072
3340
37
3
10
JiDong
32550
38068
29408
28979
5518
3142
3571
17
10
11
JhuZihJiao
24302
21529
23043
22071
2773
1259
2231
11
5
9
JianShan
26262
32897
27935
22429
6635
1673
3833
25
6
15
SinFa
47935
42159
48644
41295
5776
709
6640
12
1
14
DaJin
40181
47608
39683
36092
7427
498
4089
18
1
10
YuYouShan
72039
63584
74076
58778
8455
2037
13261
12
3
18
GaoJhong
40858
42227
43422
37294
1369
2564
3564
3
6
9
FuSing
33084
32053
34319
30836
1031
1235
2248
3
4
7
SiaoGuanShan
41586
37535
47868
40691
4051
6282
895
10
15
2
SiNan
46899
48164
64244
53285
1265
17345
6386
3
37
14
MeiShan
33285
31932
38104
34153
1353
4819
868
4
14
3
NanTienChih
44225
45067
43594
41766
842
631
2459
2
1
6
PaiYun
50065
33522
34348
35002
16543
15717
15063
33
31
30
NanSi
24998
29183
28933
32542
4185
3935
7544
17
16
30
Ali
35257
30350
39240
36458
4907
3983
1201
14
11
3
MaJia
64926
48576
60070
48896
16350
4856
16030
25
7
25
LiGang
27605
23403
27095
25301
4202
510
2304
15
2
8
PingTung
32927
40740
28894
26936
7813
4033
5991
24
12
18
SinWei
36733
41425
31463
28437
4692
5270
8296
13
14
23
LinLuo
32012
37356
30299
28563
5344
1713
3449
17
5
11
NaJhou
20852
25828
19294
19137
4976
1558
1715
24
7
8
ChaoJhou
27321
17221
24589
22796
10100
2732
4525
37
10
17
FangLiao
16425
13834
16895
15745
2591
470
680
16
3
4
MaoBiTou
22740
19711
23591
21800
3029
851
940.1
13
4
4
JyuCheng
23929
16625
16332
19319
7304
7597
4610
31
32
19
LaiYi
43166
33328
35225
31933
9838
7941
11233
23
18
26
ChiShan
41204
50232
42742
34806
9028
1538
6398
22
4
16
SanDiMan
42442
52468
37553
33943
10026
4889
8499
24
12
20
LongCyuan
34742
28349
33969
31908
6393
773
2834
18
2
8
LiLi
26451
20600
25869
24221
5851
582
2230
22
2
8
ChunMi
19299
25072
20443
20280
5773
1144
981
30
6
5
FangShan
20485
22368
18648
19564
1883
1837
921
9
9
4
FongGang
17706
21686
17516
18225
3980
190
519
22
1
3
ShangDeWun
54945
53340
53694
46476
1605
1251
8469
3
2
15
GuSia
35280
26490
35055
34041
8790
225
1239
25
1
4
WeiLiaoShan
61679
64075
61211
49864
2396
468
11815
4
1
19
SyuHai
28585
23858
24509
27186
4727
4076
1399
17
14
5
MouDan
22589
21230
27870
26842
1359
5281
4253
6
23
19
MouDanChihShan
24154
21203
26077
29144
2951
1923
4990
12
8
21
DanMenShan
16433
12021
16171
17130
4412
262
697
27
2
4
ShouKa
24854
31692
28602
28691
6838
3748
3837
28
15
15
Max
72039
64075
74076
58778
16543
17345
16030
49
37
30
Min
16425
12021
16171
15745
842
190
454
2
1
2
Mean
32106
32960
31611
29242
5804
3059
4222
19
10
12
CV
0.39
0.36
0.41
0.34
0.61
1.07
0.87
0.56
0.87
0.59
∗Estimated annual mean R factor using daily rainfall model. (Rd=0.5Pd1.66).
**Estimated annual mean R factor using monthly rainfall model. (Rm=0.6Pm1.49).
***Estimated annual mean R factor using annual rainfall model. (Ry=2.74Py1.20).Figure5 presents scatter plots showing the relationship between the Ry factors estimated at the 55 stations using the three regression models and the observed Ry factors computed using the method proposed by Wischmeier and Smith (1978). Note that, in the figures presented on the left, the x-axis represents the observed annual mean rainfall erosivity factor while the y-axis represents the estimated annual mean Ry factor. Furthermore, the individual data points indicate the annual average rainfall erosivity at the different rainfall stations. The three figures presented on the right of Figure 5 show the residual distribution as a function of the annual rainfall erosivity for each of the three models. However, that of the daily regression model deviates farther from the normal line in Figure 5(a). Figures 5(b) and 5(c) show that a better agreement exists between the estimated and observed values of the rainfall erosivity when using the monthly and annual regression models, respectively. Overall, the results presented in Figure 5 show that, in terms of the error rate, the three regression models can be ranked as follows: daily > annual > monthly. In other words, the regression models based on annual and monthly rainfall data are more accurate than that based on daily rainfall data.Figure 5
Validation results for (a) daily, (b) monthly, and (c) annual regression models based on relationship between estimatedRy and observed Ry.
(a)
(b)
(c)According to Table3 and Figure 5, the data of estimated annual mean rainfall erosivity was underestimated by daily rainfall models, respectively. Nevertheless, Liu et al. [50] indicated that much precipitation information could be provided by daily rainfall data rather than monthly and annual ones. Different from the results of [50] in China, the rainfall event in southern Taiwan might be consistent for several days, and an underestimate could be therefore produced as daily rainfall data was used to estimate erosivity.


### 3.3. Spatial Distribution Comparison of Three Regression Models

Figure6 presents the annual rainfall erosivity (Ry) and MAPE maps for each of the three regression models. Note that the observed annual rainfall erosivity map is also presented for comparison purposes. The annual rainfall erosivity (Ry) map was based on annual average rainfall erosivity recorded at the 55 rainfall stations, and it leads to the comparison between spatial distribution of the annual rainfall amount and the geographic distribution of annual rainfall erosivity. It is seen that the spatial distributions of the estimated and observed values of Ry are similar. However, for each regression model, the estimated value of Ry is slightly lower than the observed value due to statistical errors. In addition, a comparison of Figures 6(b)~6(d) confirms that the monthly rainfall model yields a better estimation performance than the daily or annual model.Figure 6
Rainfall erosivity maps and mean absolute percentage error (MAPE) maps for three estimation models: (a) observed, (b) daily, (c) monthly, and (d) annual models.
(a)
(b)
(c)
(d)


## 3.1. Relationship between Rainfall Parameters and Rainfall Erosivity

Figures3(a)~3(d) show the relationships between the event rainfall amount and the event rainfall erosivity, the daily rainfall amount and the daily rainfall erosivity, the monthly rainfall amount and the monthly rainfall erosivity, and the annual rainfall amount and the annual rainfall erosivity, respectively. In general, the results show that the rainfall erosivity varies from one geographic location to another, even under the same annual rainfall conditions. Figure 3(a) is one scatter plot of rainfall (Pj) and rainfall erosivity (Rj) that shows a significant nonlinear relationship (Rj=0.73Pj1.54,r2=0.80) between the event rainfall amount (Pj) and the event rainfall erosivity (Rj). Similarly, Figure 3(b) shows a significant relationship (Rd=0.50Pd1.66,r2=0.82) between the daily rainfall amount (Pd) and the daily rainfall erosivity (Rd). Figures 3(c) and 3(d) show that the monthly rainfall amount (Pm) and monthly rainfall erosivity (Rm) and the annual rainfall amount (Py) and the annual rainfall erosivity (Ry) are also related; that is, Rm=0.60Pm1.49, r2=0.91, and Ry=2.74Py1.20, r2=0.73, respectively. In other words, irrespective of the time interval considered, a relationship exists between the rainfall amount and the rainfall erosivity. Comparing the four intervals, it is seen that the strongest correlation exists between the monthly rainfall amount and the monthly rainfall erosivity.Figure 3
Scatter plots of (a) rainfall event amount (Pj) and rainfall event erosivity (Rj), (b) daily rainfall amount (Pd) and daily rainfall erosivity (Rd), (c) monthly rainfall amount (Pm) and monthly rainfall erosivity (Rm), and (d) annual rainfall amount (Py) and annual rainfall erosivity (Ry).
(a)
(b)
(c)
(d)Table2 shows the mean, minimum, maximum, and CV values of the annual rainfall amount and annual rainfall erosivity at each of the 55 rainfall stations over the considered time period (2002~2011). From inspection, the average annual mean rainfall over the 55 stations is equal to 2237 mm. Moreover, the minimum annual rainfall of 491 mm was recorded at the SyuHai station in 2002, while the maximum annual rainfall of 6224 mm was recorded at the YuYouShan station in 2005. The annual mean rainfall erosivity over all 55 rainfall stations is equal to 31118 MJ mm ha−1 h−1 yr−1. In addition, the minimum rainfall erosivity of 2271 MJ mm ha−1 h−1 yr−1 was measured at the DanMenShan station in 2002, while the maximum rainfall erosivity of 142370 MJ mm ha−1 h−1 yr−1 was measured at the YuYouShan station in 2005.Table 2
Annual rainfall and annual rainfall erosivity data (2002~2011) for 55 rainfall stations in southern Taiwan.
Number
Rainfall station
Annual rainfall (mm)
Annual rainfall erosivity (MJ mm ha−1 h−1 yr−1)
Regression models
r
2
Max
Min
Mean
CV
Max
Min
Mean
CV
1
ZuoYing
2373
700
1602
0.35
33723
7937
22454
0.35
R
y = 33.47P0.88
0.62
2
FongSen
2253
889
1616
0.31
39689
7512
22072
0.43
R
y = 66.47P0.78
0.29
3
SaYe
2373
1306
1736
0.23
33723
16132
23135
0.26
R
y = 0.90P1.36
0.71
4
GangShan
2671
909
1617
0.38
46687
8273
20975
0.61
R
y = 2.23P1.25
0.74
5
GuTingKeng
2656
537
1421
0.49
38869
5033
17198
0.63
R
y = 1.65P1.26
0.95
6
MuJha
4461
1412
2154
0.43
59574
16691
23355
0.52
R
y = 1.17P1.31
0.93
7
CiShan
3057
1091
1996
0.35
40927
13247
24545
0.40
R
y = 15.17P0.97
0.73
8
FongSyong
2814
881
1772
0.34
41035
10802
25122
0.42
R
y = 9.42P1.05
0.64
9
Jiashian
4461
1506
2650
0.39
76637
15779
41555
0.53
R
y = 3.10P1.20
0.75
10
SiBu
2981
982
1903
0.34
49680
10644
27468
0.50
R
y = 0.59P1.42
0.86
11
FongShan
2672
867
1787
0.33
37336
11659
24753
0.38
R
y = 6.92P1.09
0.77
12
DaLiao
2454
821
1723
0.31
32686
7103
22962
0.38
R
y = 3.68P1.17
0.66
13
YueMei
3598
1410
2271
0.28
41677
17889
25374
0.33
R
y = 17.90P0.95
0.74
14
MeiNong
3399
1083
2227
0.35
59758
16033
31859
0.49
R
y = 5.62P1.12
0.81
15
JiDong
3221
1171
2257
0.30
47197
18988
32550
0.29
R
y = 684.83P0.50
0.30
16
JhuZihJiao
2848
876
1799
0.36
49183
7989
24302
0.55
R
y = 9.36P1.05
0.53
17
JianShan
3063
632
1823
0.39
60047
6044
26262
0.58
R
y = 1.27P1.32
0.86
18
SinFa
4589
1630
3032
0.34
75976
21836
47935
0.44
R
y = 4.47P1.15
0.76
19
DaJin
4105
1322
2710
0.32
66543
13987
40181
0.42
R
y = 0.95P1.34
0.83
20
YuYouShan
6224
1767
4070
0.34
142370
19412
72039
0.50
R
y = 0.43P1.44
0.88
21
GaoJhong
4565
1188
2785
0.40
69908
12387
40858
0.54
R
y = 1.28P1.30
0.72
22
FuSing
4231
1077
2377
0.46
81114
7355
33084
0.73
R
y = 0.81P1.35
0.65
23
SiaoGuanShan
4164
1697
2995
0.26
93739
14726
41586
0.54
R
y = 0.16P1.55
0.66
24
SiNan
5557
1800
3750
0.32
98956
13550
46899
0.59
R
y = 1.50P1.25
0.54
25
MeiShan
4270
1122
2589
0.39
69331
10799
33285
0.65
R
y = 0.25P1.49
0.77
26
NanTienChih
4986
1615
3661
0.33
101544
9538
41011
0.73
R
y = 0.02P1.74
0.73
27
PaiYun
3844
1294
2642
0.32
33848
6862
18175
0.48
R
y = 0.45P1.33
0.79
28
NanSi
3572
1230
2672
0.33
48871
6949
24998
0.56
R
y = 0.033P1.72
0.86
29
ALi
4049
1661
2733
0.34
59940
15606
35257
0.51
R
y = 0.35P1.45
0.86
30
MaJia
5530
1820
3491
0.35
122022
25807
64926
0.50
R
y = 6.25P1.12
0.64
31
LiGang
3142
1201
2016
0.32
39945
12491
27605
0.33
R
y = 23.31P0.93
0.62
32
PingTung
3351
990
2124
0.34
65988
10229
32927
0.50
R
y = 1.84P1.27
0.76
33
SinWei
3999
1312
2222
0.37
87155
13318
36733
0.60
R
y = 2.38P1.24
0.64
34
LinLuo
3267
1139
2230
0.30
53448
17799
32012
0.34
R
y = 51.92P0.83
0.61
35
NaJhou
2340
773
1597
0.33
33690
9998
20852
0.38
R
y = 43.40P0.83
0.54
36
ChaoJhou
2581
811
1848
0.32
52474
6426
27321
0.49
R
y = 0.97P1.35
0.66
37
FangLiao
2311
534
1376
0.47
28044
4763
16425
0.50
R
y = 8.67P1.03
0.81
38
MaoBiTou
2050
998
1419
0.21
99535
10631
22740
1.19
R
y = 0.002P2.19
0.49
39
JyuCheng
2218
986
1610
0.26
62730
7558
23929
0.70
R
y = 0.07P1.71
0.64
40
LaiYi
3439
1556
2448
0.24
82126
21753
43166
0.47
R
y = 10.17P1.06
0.36
41
ChiShan
3714
1347
2630
0.28
67586
15140
41204
0.38
R
y = 4.87P1.14
0.61
42
SanDiMan
3773
1655
2575
0.26
75709
20727
42442
0.44
R
y = 1.27P1.32
0.64
43
LongCyuan
3653
1249
2438
0.31
65942
12170
34742
0.44
R
y = 2.27P1.23
0.67
44
LiLi
2864
1137
1944
0.31
39750
12995
26451
0.38
R
y = 17.46P0.96
0.56
45
ChunMi
2615
847
1677
0.33
32659
7211
19299
0.45
R
y = 1.82P1.24
0.75
46
FangShan
2281
1074
1627
0.27
66431
8886
20485
0.81
R
y = 0.17P1.56
0.58
47
FongGang
1972
849
1534
0.27
37847
5489
17706
0.49
R
y = 0.77P1.36
0.68
48
ShangDeWun
2671
909
1700
0.33
42345
11248
54945
0.16
R
y = 17.34P0.99
0.59
49
GuSia
3495
1598
2582
0.27
48113
16361
35280
0.32
R
y = 2.78P1.20
0.73
50
WeiLiaoShan
5666
1377
3548
0.40
121787
14042
61679
0.52
R
y = 2.66P1.23
0.87
51
SyuHai
2939
491
2022
0.37
53235
4231
28585
0.49
R
y = 2.14P1.21
0.88
52
MouDan
2661
1396
2118
0.20
50943
13706
22589
0.50
R
y = 0.50P1.41
0.56
53
MouDanChihShan
3377
1577
2268
0.26
53046
13279
24154
0.52
R
y = 0.99P1.30
0.50
54
DanMenShan
2129
558
1457
0.41
30074
2271
16433
0.49
R
y = 10.52P
0.48
55
ShouKa
2606
1735
2184
0.16
28325
10158
24854
0.20
R
y = 1.24P1.25
0.52An inspection of Table2 shows that the correlation coefficients (r2) between the mean annual rainfall and the rainfall erosivity range from 0.29 to 0.95. Moreover, 49 of the 55 stations have a correlation coefficient (r2) greater than 0.5, which are satisfied by a significance test (two-tailed test) with a 99% confidence level (P value < 0.01). The CV values of the annual rainfall range from 0.16 to 0.49, while those of the annual rainfall erosivity range from 0.16 to 1.19. Of all the stations, the GuTingKeng station has the highest CV  (0.49) for the annual rainfall, while the MaoBiTou station has the highest CV  (1.19) for the annual rainfall erosivity.GIS (Geographic Information System) was used to interpolate and plot the spatial variability of the annual rainfall erosivity factor (Ry) over the study area using the Kriging interpolation method [16]. Figures 4(a) and 4(b) show the results obtained for the annual rainfall and annual erosivity, respectively. An inspection of Figure 4(a) shows that the mean annual total rainfall ranges from 1376 to 4070 mm yr−1. Based on the regression relationship for the annual rainfall (Ry=2.74Py1.20), the rainfall gradient values range from 14785 to 72039 MJ mm ha−1h−1yr−1. Moreover, the Kriging interpolation results show that the annual rainfall erosivity has a west-east gradient with values ranging from 15000 to 70000 MJ mm ha−1 h−1 yr−1. It is seen that the spatial distributions of the annual rainfall and annual rainfall erosivity, respectively, are similar. Different interpolation methods may result in different spatial distributions of the rainfall erosivity. However, Angulo-Martínez and Beguería [33] found that all common interpolation methods are capable of capturing the regional distribution of the R factor given the use of a spatially dense rainfall database with a high temporal resolution.Figure 4
(a) Annual precipitation and (b) annual rainfall erosivity maps in southern Taiwan. Note that isohyet and isoerodent intervals are 500 mm and 10000 MJ mm ha−1 h−1 yr−1, respectively.
(a)
(b)The rainfall erosivity map presented in Figure4(b) is of great relevance for soil erosion evaluation and control. It has implications not only for agriculture but also for many activities related to land use planning. Furthermore, it can be used as a guide for soil conservation practices and landscape modeling since the R factor is usually an important part of erosion models such as the USLE [16].The higher erosivity observed in the tropic region is caused by the high amount of precipitation, intensity, and kinetic energy of rain. The main generating mechanism of rainfall is convection effect in most tropical regions. As a result, the regions receive more rain with higher intensities than the temperate regions, dominated by midlatitude cyclones [41].The regression models to estimate rainfall erosivity for specific locations are unable to accurately predict actual rainfall erosivity for other locations due to site-specific conditions. Therefore, simplified methods based on annual precipitation for estimating rainfall erosivity should be used with caution according to location or time period. Their results deserve careful attention as applying simplified methods to estimating annual rainfall erosivity.


## 3.2. Applicability of Three Regression Models

The applicability of the daily, monthly, and annual regression models developed in the previous subsection (i.e.,Rd=0.50Pd1.66, Rm=0.60Pm1.49, and Ry=2.74Py1.20, resp.) was evaluated by comparing the results obtained from each model for the rainfall erosivity factor with the observed rainfall erosivity factor computed using the method presented by Wischmeier and Smith [7]. Table 3 presents the RMSE and MAPE analysis results for the estimated and observed rainfall erosivity values. It is seen that when estimating the Ry factor using (3) based on the daily rainfall data, the MAPE ranges from 2% to 49% (CV=0.50) and the RMSE varies from 1031 to 16350 MJ mm ha−1 h−1 yr−1 (CV=0.55). Similarly, when estimating the Ry factor using the monthly rainfall data, the MAPE ranges from 1% to 37% (CV=0.87), while the RMSE varies from 190 to 17345 MJ mm ha−1 h−1 yr−1 (CV=0.96). Finally, when estimating the Ry factor based on the annual rainfall data, the MAPE ranges from 2% to 30% (CV=0.59) and the RMSE varies from 454 to 16030 MJ mm ha−1h−1yr−1 (CV=0.85). Overall, it can be seen that the estimation errors of the three models range from 11% to 49%. For the daily model, the error rate exceeds 10% at 11 of the 55 stations. However, for the monthly and annual regression models, the error rate is less than 10% for 34 and 24 of the 55 stations, respectively.Table 3
Comparison of estimated rainfall erosivity factorRy and observed rainfall erosivity factor Ry (unit: MJ mm ha−1 h−1 yr−1).
Rainfall station
R
y
R
y
∗
R
y
∗
∗
R
y
∗
∗
∗
RMSE*
RMSE**
RMSE***
MAPE*
MAPE**
MAPE***
ZuoYing
22454
26889
18927
19208
4435
3527
3246
20
16
14
FongSen
22072
25814
16576
19409
3742
5496
2663
17
25
12
SaYe
23135
27360
20807
19680
4225
2328
3455
18
10
15
GangShan
20975
19239
18767
19412
1736
2208
1563
8
11
7
GuTingKeng
17198
25627
20154
16625
8429
2956
573
49
17
3
MuJha
23355
32082
22104
25164
8727
1251
1809
37
5
8
CiShan
24545
27016
26060
24999
2471
1515
454
10
6
2
FongSyong
25122
33138
22358
21677
8016
2764
3445
32
11
14
Jiashian
41555
50785
40394
35132
9230
1161
6423
22
3
15
SiBu
27468
37029
25515
23613
9561
1953
3855
35
7
14
FongShan
24753
30880
22707
21887
6127
2046
2866
25
8
12
DaLiao
22962
29446
21045
20955
6484
1917
2007
28
8
9
YueMei
25374
35168
31863
29181
9794
6489
3807
39
26
15
MeiNong
31859
43738
30787
28519
11879
1072
3340
37
3
10
JiDong
32550
38068
29408
28979
5518
3142
3571
17
10
11
JhuZihJiao
24302
21529
23043
22071
2773
1259
2231
11
5
9
JianShan
26262
32897
27935
22429
6635
1673
3833
25
6
15
SinFa
47935
42159
48644
41295
5776
709
6640
12
1
14
DaJin
40181
47608
39683
36092
7427
498
4089
18
1
10
YuYouShan
72039
63584
74076
58778
8455
2037
13261
12
3
18
GaoJhong
40858
42227
43422
37294
1369
2564
3564
3
6
9
FuSing
33084
32053
34319
30836
1031
1235
2248
3
4
7
SiaoGuanShan
41586
37535
47868
40691
4051
6282
895
10
15
2
SiNan
46899
48164
64244
53285
1265
17345
6386
3
37
14
MeiShan
33285
31932
38104
34153
1353
4819
868
4
14
3
NanTienChih
44225
45067
43594
41766
842
631
2459
2
1
6
PaiYun
50065
33522
34348
35002
16543
15717
15063
33
31
30
NanSi
24998
29183
28933
32542
4185
3935
7544
17
16
30
Ali
35257
30350
39240
36458
4907
3983
1201
14
11
3
MaJia
64926
48576
60070
48896
16350
4856
16030
25
7
25
LiGang
27605
23403
27095
25301
4202
510
2304
15
2
8
PingTung
32927
40740
28894
26936
7813
4033
5991
24
12
18
SinWei
36733
41425
31463
28437
4692
5270
8296
13
14
23
LinLuo
32012
37356
30299
28563
5344
1713
3449
17
5
11
NaJhou
20852
25828
19294
19137
4976
1558
1715
24
7
8
ChaoJhou
27321
17221
24589
22796
10100
2732
4525
37
10
17
FangLiao
16425
13834
16895
15745
2591
470
680
16
3
4
MaoBiTou
22740
19711
23591
21800
3029
851
940.1
13
4
4
JyuCheng
23929
16625
16332
19319
7304
7597
4610
31
32
19
LaiYi
43166
33328
35225
31933
9838
7941
11233
23
18
26
ChiShan
41204
50232
42742
34806
9028
1538
6398
22
4
16
SanDiMan
42442
52468
37553
33943
10026
4889
8499
24
12
20
LongCyuan
34742
28349
33969
31908
6393
773
2834
18
2
8
LiLi
26451
20600
25869
24221
5851
582
2230
22
2
8
ChunMi
19299
25072
20443
20280
5773
1144
981
30
6
5
FangShan
20485
22368
18648
19564
1883
1837
921
9
9
4
FongGang
17706
21686
17516
18225
3980
190
519
22
1
3
ShangDeWun
54945
53340
53694
46476
1605
1251
8469
3
2
15
GuSia
35280
26490
35055
34041
8790
225
1239
25
1
4
WeiLiaoShan
61679
64075
61211
49864
2396
468
11815
4
1
19
SyuHai
28585
23858
24509
27186
4727
4076
1399
17
14
5
MouDan
22589
21230
27870
26842
1359
5281
4253
6
23
19
MouDanChihShan
24154
21203
26077
29144
2951
1923
4990
12
8
21
DanMenShan
16433
12021
16171
17130
4412
262
697
27
2
4
ShouKa
24854
31692
28602
28691
6838
3748
3837
28
15
15
Max
72039
64075
74076
58778
16543
17345
16030
49
37
30
Min
16425
12021
16171
15745
842
190
454
2
1
2
Mean
32106
32960
31611
29242
5804
3059
4222
19
10
12
CV
0.39
0.36
0.41
0.34
0.61
1.07
0.87
0.56
0.87
0.59
∗Estimated annual mean R factor using daily rainfall model. (Rd=0.5Pd1.66).
**Estimated annual mean R factor using monthly rainfall model. (Rm=0.6Pm1.49).
***Estimated annual mean R factor using annual rainfall model. (Ry=2.74Py1.20).Figure5 presents scatter plots showing the relationship between the Ry factors estimated at the 55 stations using the three regression models and the observed Ry factors computed using the method proposed by Wischmeier and Smith (1978). Note that, in the figures presented on the left, the x-axis represents the observed annual mean rainfall erosivity factor while the y-axis represents the estimated annual mean Ry factor. Furthermore, the individual data points indicate the annual average rainfall erosivity at the different rainfall stations. The three figures presented on the right of Figure 5 show the residual distribution as a function of the annual rainfall erosivity for each of the three models. However, that of the daily regression model deviates farther from the normal line in Figure 5(a). Figures 5(b) and 5(c) show that a better agreement exists between the estimated and observed values of the rainfall erosivity when using the monthly and annual regression models, respectively. Overall, the results presented in Figure 5 show that, in terms of the error rate, the three regression models can be ranked as follows: daily > annual > monthly. In other words, the regression models based on annual and monthly rainfall data are more accurate than that based on daily rainfall data.Figure 5
Validation results for (a) daily, (b) monthly, and (c) annual regression models based on relationship between estimatedRy and observed Ry.
(a)
(b)
(c)According to Table3 and Figure 5, the data of estimated annual mean rainfall erosivity was underestimated by daily rainfall models, respectively. Nevertheless, Liu et al. [50] indicated that much precipitation information could be provided by daily rainfall data rather than monthly and annual ones. Different from the results of [50] in China, the rainfall event in southern Taiwan might be consistent for several days, and an underestimate could be therefore produced as daily rainfall data was used to estimate erosivity.


## 3.3. Spatial Distribution Comparison of Three Regression Models

Figure6 presents the annual rainfall erosivity (Ry) and MAPE maps for each of the three regression models. Note that the observed annual rainfall erosivity map is also presented for comparison purposes. The annual rainfall erosivity (Ry) map was based on annual average rainfall erosivity recorded at the 55 rainfall stations, and it leads to the comparison between spatial distribution of the annual rainfall amount and the geographic distribution of annual rainfall erosivity. It is seen that the spatial distributions of the estimated and observed values of Ry are similar. However, for each regression model, the estimated value of Ry is slightly lower than the observed value due to statistical errors. In addition, a comparison of Figures 6(b)~6(d) confirms that the monthly rainfall model yields a better estimation performance than the daily or annual model.Figure 6
Rainfall erosivity maps and mean absolute percentage error (MAPE) maps for three estimation models: (a) observed, (b) daily, (c) monthly, and (d) annual models.
(a)
(b)
(c)
(d)


## 4. Conclusions

The rainfall erosivity factor (R) is one of the key factors in the USLE model and has gained increasing importance as the environmental effects of climate change have become more severe. This study has proposed three models for estimating the value of R based on daily, monthly, and annual precipitation data of rainfall station network, respectively. The validity of the three models has been evaluated using the rainfall data collected over a period of ten yrs (2002~2011) at 55 rainfall stations in southern Taiwan. The results have shown that, of the three models, the annual and monthly models yield a better agreement with the observed rainfall erosivity factor than the daily model.



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*Source: 214708-2015-06-08.xml*