research article evaluation of annual rainfall...

Research ArticleEvaluation of Annual Rainfall Erosivity Index Based onDaily Monthly and Annual Precipitation Data of RainfallStation Network in Southern Taiwan

Ming-Hsi Lee1 and Huan-Hsuan Lin2

1Department of Soil and Water Conservation National Pingtung University of Science and Technology Pingtung 912 Taiwan2Department of Civil Engineering National Pingtung University of Science and Technology Pingtung 912 Taiwan

Correspondence should be addressed to Ming-Hsi Lee mhleemailnpustedutw

Received 20 August 2014 Accepted 15 October 2014

Academic Editor Joe-Air Jiang

Copyright copy 2015 M-H Lee and H-H Lin This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The erosivity factor in the universal soil loss equation (USLE) provides an effective means of evaluating the erosivity power ofrainfall The present study proposes three regression models for estimating the erosivity factor based on daily monthly and annualprecipitation data of rainfall station network respectively The validity of the proposed models is investigated using a datasetconsisting of 16560 storm events monitored by 55 rainfall stations in southern Taiwan The results show that for 49 of the 55stations a strong positive correlation (1199032 gt 05) exists between the annual rainfall amount and the annual rainfall erosivity factorIn other words the estimation model based on the annual precipitation data provides a reliable means of predicting the long-termannual rainfall erosivity in southern Taiwan Furthermore the root mean square error (RMSE) andmean absolute percentage error(MAPE) analysis results show that the estimation models based on annual and monthly precipitation data have a more accurateprediction performance than that based on daily precipitation data

1 Introduction

Water erosion is one of the most important worldwide envi-ronmental concerns particularly in tropical and subtropicalregions of the world such as Taiwan One of the mostimportant active agents of soil erosion is rain due to itspotential for producing soil disaggregation and subsequentremoval The effects of raindrop impact and surface runoffon soil erosion are generally estimated using the universal soilloss equation (USLE) [1] namely

119860 = 119877119870119871119878119862119875 (1)

where 119860 is the rate of soil loss (ton haminus1 yrminus1) 119877 is theannual rainfall erosivity factor (MJmmhaminus1 hminus1 yrminus1) 119870 isthe soil erodibility factor (t ha yr haminus1MJminus1mmminus1) 119871 is theslope length factor 119878 is the slope steepness factor 119862 isthe cover and management factor and 119875 is the supportingpractices factor [2 3] Amongst these factors the erosivityfactor (119877) 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] 119877 is calculated as the productof the storm rainfall energy (119864) and the maximum 30-minrainfall intensity (119868

30) However Wischmeier and Smith [7]

also defined 119877 as the average of the annual summations of the11986411986830

values for all storm events yielding more than 127mmof rainfall

The rainfall erosivity index 119877 describes the erosiveimpact of rainfall and runoff on both the detachment and theentrainment of soil and is given as [1]

119877119895= 119864119895times 11986811989530=

119879119894

sum119894=1

(119890119894119875119895119894) times 11986811989530 (2)

where119864119895is the kinetic energy (MJmm) 119868

11989530is themaximum

30-min rainfall intensity (mmh) 119890119894is the unitary kinetic

energy (MJmmsdotha) 119875119895119894is the rainfall amount (mm) and 119879

119894

is the total rainfall duration Note that the subscripts 119894 and 119895denote the number of rainfall data instances and the number

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 214708 15 pageshttpdxdoiorg1011552015214708

2 International Journal of Distributed Sensor Networks

of rainfall events respectively Summing the rainfall erosivityindex of all the rainfall events over one year the annualrainfall erosivity index can be obtained as

119877119910=

119884

sum119895=1

119877119895 (3)

where 119884 is the number of rainfall events in the year Inaddition the unitary kinetic energy 119890

119894is deduced from the

relationship between the raindrop diameter and the rainfallintensity as follows [8]

119864119894=

0119 + 00873 log 119868119894

for 119868119894lt 76mmhr

0283 for 119868119894ge 76mmhr

(4)

The rainfall erosivity index 119877 has been widely testedand applied in many countries and regions around the worldwhose rainfall intensity is characterized mainly as moderateto high [9ndash15] In computing the rainfall erosivity factorthe maximum 30-min rainfall intensities for the storm andheavy storm events are generally computed on the basis ofhyetograph data or high-resolution rainfall data (pluviographdata) Generally speaking pluviograph data for at least 20 yrsare required to compute the rainfall erosivity for a given studyarea using the (119877) USLE formulation [2] However such largevolumes of data are not available for all regions of the worldFurthermore even if sufficient pluviograph data are availablecomputing the rainfall erosivity is a complicated and tedioustask To overcome this problem various simplified modelshave been proposed for estimating the rainfall erosivity factorusing more readily available precipitation data

Among suchmodels those based on annual precipitationdata are particularly common since annual rainfall data areavailable in most regions of the world and tend to be fairlyreliable Furthermore various studies have shown that a goodcorrelation exists between the annual rainfall erosivity andthe annual precipitation amount at many locations aroundtheworld [16 17] Accordingly annual precipitation data havebeen used to obtain simple estimates of the rainfall erosivityin many countries [2 11 18ndash34]

Several researchers have used both annual precipitationdata and maximum daily and hourly precipitation data toestimate the rainfall erosivity factor in the Mediterraneanregion [35 36] However the models used in these studiesestimate the mean annual rainfall erosivity over severalyrs rather than the rainfall erosivity in a particular yrMany regression models based on variations in the observedrainfall erosivity or seasonal erosivity have been proposedfor predicting the daily rainfall erosivity [15 33 37ndash44] ormonthly rainfall erosivity [45 46] It has been shown thatthe use of daily or monthly rainfall records provides a betterunderstanding of the rainfall erosivity of individual stormsthan annual precipitation data [34] In constructing daily ormonthly prediction models it is necessary to compute therainfall erosivity on a daily or monthly basis respectivelyHowever calculating the daily and monthly rainfall erosivityis more challenging than computing that for a particularstorm For example if it rains from May 31 to June 1

the observed rainfall erosivity for this storm has just onevalue However the corresponding data should be dividedinto two different values (ie daily or monthly segments)when constructing daily ormonthlymodelsThus the annualsum of the reclassified rainfall erosivity is different from theobserved value due to the use of different boundary con-ditions Moreover the daily or monthly rainfall parametersused in daily and monthly models respectively provide aninadequate description of the kinetic energy and rainfallintensity terms in the rainfall erosivity index [33 47]

Although annual regression models are a gross oversim-plification of the observed variation in the rainfall erosivityand their estimated values are rough [33 48] they never-theless represent a viable alternative to detailed quantitativeassessments in providing a long-term assessment of theannual mean rainfall erosivity using the USLE formulation[49] Thus as discussed above numerous researchers haveproposed methods for estimating the rainfall erosivity basedon annual precipitation data andor other rainfall parametersHowever such models require careful optimization andcalibration for each specific location and include site-specificcoefficients The proposed study is to find out the suitablemodels among daily monthly and annual precipitation data

The present study proposes three regression models forestimating the rainfall erosivity and finding out the suitablemodels in southern Taiwan based on daily monthly andannual precipitation data of rainfall station network respec-tively even without 30-min rainfall dataThe detailed goals ofthis study can be summarized as follows (a) to construct newmodels for the large-scale estimation of the erosivity factor insouthern Taiwan and (b) to analyze the spatial distribution ofthe daily monthly and annual rainfall erosivity in southernTaiwan

2 Materials and Methods

21 Study Area This study considered the regions of Kaohsi-ung City and Pingtung County in southern Taiwan The tworegions cover areas of 2961 km2 and 2784 km2 respectivelyand contain a total of 55 rainfall stations (see Figure 1) Bothregions commonly experience extreme rainfall events duringthe summer months For example in August 2009 TyphoonMorakot resulted in catastrophic damage that left 665 peopledead 34 others missing and roughly US$ 44 billion indamages

22 Rainfall Data Table 1 summarizes the basic geographicand rainfall data of the 28 rainfall stations in Kaohsiung Cityand 27 rainfall stations in Pingtung County over the 10 yrperiod extending from 2002 to 2011 Traditionally the high-resolution rainfall data recorded by each station in Table 1 areused to calculate the rainfall erosivity factor in accordancewith (2)ndash(4) [7] In the present study the reliability of thesedata was evaluated using the 10-min rainfall data obtainedfor the corresponding period from the Central WeatherBureau (CWB) of Taiwan In the present study 16560 stormevents were selected from the 550 observed annual rainfalldatasets presented in Table 1 (ie 55 stations times 10 yrs) Thecorresponding daily monthly and annual rainfall data were

International Journal of Distributed Sensor Networks 3

Table 1 Geographic and rainfall data (2002sim2011) for 55 rainfall stations in southern Taiwan

Number Rainfall station Latitude Longitude Referenceperiod (yr) Elevation (m) Storm events Annual

rainfall (mm)1 ZuoYing 120∘171015840N 22∘401015840E 10 13 230 16022 FongSen 120∘231015840N 22∘321015840E 10 61 241 16163 SaYe 120∘161015840N 22∘501015840E 10 35 366 17364 GangShan 120∘171015840N 22∘451015840E 10 31 259 16175 GuTingKeng 120∘241015840N 22∘531015840E 10 87 259 14216 MuJha 120∘271015840N 22∘581015840E 10 94 224 21547 CiShan 120∘291015840N 22∘521015840E 10 63 421 19968 FongSyong 120∘211015840N 22∘451015840E 10 55 290 17729 Jiashian 120∘351015840N 23∘041015840E 10 60 232 265010 SiBu 120∘261015840N 22∘431015840E 10 30 255 190311 FongShan 120∘211015840N 22∘381015840E 10 27 377 178712 DaLiao 120∘251015840N 22∘361015840E 10 24 302 172313 YueMei 120∘321015840N 22∘581015840E 10 112 212 227114 MeiNong 120∘311015840N 22∘531015840E 10 46 307 222715 JiDong 120∘331015840N 22∘501015840E 10 95 314 225716 JhuZihJiao 120∘201015840N 22∘481015840E 10 51 310 179917 JianShan 120∘221015840N 22∘481015840E 10 270 313 182318 SinFa 120∘391015840N 23∘031015840E 10 470 256 303219 DaJin 120∘381015840N 22∘531015840E 10 190 427 271020 YuYouShan 120∘421015840N 23∘001015840E 10 1637 381 407021 GaoJhong 120∘431015840N 23∘081015840E 10 760 241 278522 FuSing 120∘481015840N 23∘131015840E 10 700 380 237723 SiaoGuanShan 120∘481015840N 23∘091015840E 10 1781 355 299524 SiNan 120∘481015840N 23∘041015840E 10 1792 274 375025 MeiShan 120∘491015840N 23∘161015840E 10 860 319 258926 NanTienChih 120∘541015840N 23∘161015840E 10 2700 291 366127 PaiYun 120∘571015840N 23∘271015840E 10 3340 238 264228 NanSi 120∘531015840N 23∘261015840E 10 1949 438 267229 ALi 120∘441015840N 22∘441015840E 10 1040 263 273330 MaJia 120∘411015840N 22∘401015840E 10 740 248 349131 LiGang 120∘291015840N 22∘471015840E 10 42 310 201632 PingTung 120∘301015840N 22∘391015840E 10 25 292 212433 SinWei 120∘321015840N 22∘451015840E 10 56 352 222234 LinLuo 120∘331015840N 22∘391015840E 10 54 234 223035 NaJhou 120∘301015840N 22∘291015840E 10 20 306 159736 ChaoJhou 120∘321015840N 22∘321015840E 10 12 354 184837 FangLiao 120∘351015840N 22∘211015840E 10 69 305 137638 MaoBiTou 120∘441015840N 21∘551015840E 10 49 342 141939 JyuCheng 120∘441015840N 22∘041015840E 10 54 320 161040 LaiYi 120∘371015840N 22∘311015840E 10 74 363 244841 ChiShan 120∘361015840N 22∘351015840E 10 48 284 263042 SanDiMan 120∘381015840N 22∘421015840E 10 59 245 257543 LongCyuan 120∘361015840N 22∘401015840E 10 61 333 243844 LiLi 120∘371015840N 22∘251015840E 10 91 228 194445 ChunMi 120∘371015840N 22∘221015840E 10 86 387 1677


Table 1 Continued


rainfall (mm)46 FangShan 120∘391015840N 22∘141015840E 10 36 197 162747 FongGang 120∘411015840N 22∘111015840E 10 63 307 153448 ShangDeWun 120∘421015840N 22∘451015840E 10 820 395 170049 GuSia 120∘381015840N 22∘461015840E 10 140 395 258250 WeiLiaoShan 120∘411015840N 22∘491015840E 10 1018 229 354851 SyuHai 120∘531015840N 22∘111015840E 10 20 227 202252 MouDan 120∘501015840N 22∘111015840E 10 285 273 211853 MouDanChihShan 120∘501015840N 22∘091015840E 10 504 251 226854 DanMenShan 120∘441015840N 22∘061015840E 10 260 364 145755 ShouKa 120∘511015840N 22∘141015840E 10 489 244 2184

Total 550 16560

120∘E 121∘E

235∘N

230∘N

225∘N

220∘N

Kaohsiung City

Pingtung County

Rainfall stationsStudy area

0 12500 25000 50000

(m)

S

N

W E

Figure 1 Geographic locations of 55 rainfall stations in southern Taiwan


10-minute rainfall dataof 55 rainfall stations

(2002ndash2011 year)Rainfall erosivity event

Monthly rainfall erosivityDaily rainfall erosivity Annual rainfall erosivity

rainfall data rainfall data rainfall data

Applicability of regression models(RMSE MAPE and Bias)

Spatial distribution comparison of regression models

(Kriging)

Assessment of three regression equations

(Rj)

Pj ge 127mm

(n = 2266)

Estimated Ry by daily Estimated Ry by monthly Estimated Ry by annual

Observed Ry

Rd = aPbd Rm = aPb

m Ry = aPby

Rlowasty =

Y

sumj=1

Rd =Y

sumj=1

aPbd Rlowastlowast

y =Y

sumj=1

Rm =Y

sumj=1

aPbm Rlowastlowastlowast

y =Y

sumj=1

Ry =Y

sumj=1

aPby

Ry =Y

sumj=1

Rj

Ry =Y

sumj=1

RjRd =D

sumj=1

Rj Rm =M

sumj=1

Rj

Figure 2 Flowchart of calculation

then used for analysis purposes and for constructing theestimation models

23 Validation of Models The present study developed threeregression models based on the daily monthly and annualrainfall data respectively for estimating the annual rainfallerosivity factor (119877) in southern TaiwanThe estimated valuesof 119877 were then compared with the observed erosivity factorscalculated using (2)ndash(4) [7] For each model the differencesbetween the estimated and observed values at each rainfallstation were evaluated in terms of the root mean squareerror (RMSE) and mean absolute percentage error (MAPE)computed as mentioned by Lee and Heo [17] as follows

RMSE = radic(119877obe minus 119877est)2

MAPE =100381610038161003816100381610038161003816100381610038161003816

(119877obe minus 119877est)

119877obe

100381610038161003816100381610038161003816100381610038161003816times 100 ()

(5)

where 119877obe denotes the observed rainfall erosivity factor and119877est is the estimated rainfall erosivity factor

In order to develop an accurate model for estimating therainfall erosivity it must first be determined whether or not asignificant relationship exists between the rainfall parameters

and the rainfall erosivity In identifying appropriate param-eters for predicting the annual rainfall erosivity the presentstudy considered four different rainfall parameters namelythe event rainfall amount (119875

119895) the daily rainfall amount

(119875119889) the monthly rainfall amount (119875

119898) and the annual

rainfall amount (119875119910) The correlation coefficients between

these parameters and the rainfall erosivity were calculated foreach of the 55 rainfall stations In addition the coefficientof variation (CV) of the observed annual rainfall erosivityand annual rainfall was also computed for each station inaccordance with

CV = 120590119906 (6)

where 120590 is the standard deviation and 119906 is the mean valueFigure 2 summarizes themethods to develop the regional

erosivity models from daily monthly and annual precipita-tion data

3 Results and Discussion

31 Relationship between Rainfall Parameters and RainfallErosivity Figures 3(a)sim3(d) show the relationships betweenthe event rainfall amount and the event rainfall erosivitythe daily rainfall amount and the daily rainfall erosivity


0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

N = 16560

Linear equationRj = 2088Pj (r2 = 078)Exponentiation equationRj = 073Pj

154 (r2 = 080)

Pj (mm)

Rj

(MJ m

mh

a h)

(a)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 200 400 600 800 1000 1200

N = 3616

Linear equationRd = 1914Pd (r2 = 071)Exponentiation equationRd = 050Pd

166 (r2 = 082)

Pd (mm)

Rd

(MJ m

mh

a h)

(b)

0

20000

40000

60000

80000

100000

120000

0 500 1000 1500 2000 2500 3000 3500

N = 1413

Linear equationRm= 1797Pm (r2 = 079)

Exponentiation equationRm= 060Pm

149 (r2 = 091)

Pm (mm)

Rm

(MJ m

mh

a h)

(c)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 2000 4000 6000 8000

N = 550

Linear equationRy = 1450Py (r2 = 069)Exponentiation equationRy = 274Py

120 (r2 = 073)

Py (mm)

Ry

(MJ m

mh

a h yr

)

(d)

Figure 3 Scatter plots of (a) rainfall event amount (119875119895) and rainfall event erosivity (119877

119895) (b) daily rainfall amount (119875

119889) and daily rainfall

erosivity (119877119889) (c) monthly rainfall amount (119875

119898) and monthly rainfall erosivity (119877

119898) and (d) annual rainfall amount (119875

119910) and annual rainfall

erosivity (119877119910)

the monthly rainfall amount and the monthly rainfall erosiv-ity and the annual rainfall amount and the annual rainfallerosivity respectively In general the results show that therainfall erosivity varies from one geographic location toanother even under the same annual rainfall conditionsFigure 3(a) is one scatter plot of rainfall (119875

119895) and rainfall

erosivity (119877119895) that shows a significant nonlinear relationship

(119877119895= 073119875154

119895 1199032 = 080) between the event rainfall amount

(119875119895) and the event rainfall erosivity (119877

119895) Similarly Figure 3(b)

shows a significant relationship (119877119889= 050119875166

119889 1199032 = 082)

between the daily rainfall amount (119875119889) and the daily rainfall

erosivity (119877119889) Figures 3(c) and 3(d) show that the monthly

rainfall amount (119875119898) and monthly rainfall erosivity (119877

119898) and

the annual rainfall amount (119875119910) and the annual rainfall ero-

sivity (119877119910) are also related that is 119877

119898= 060119875149

119898 1199032 = 091

and 119877119910= 274119875120

119910 1199032 = 073 respectively In other words

irrespective of the time interval considered a relationshipexists between the rainfall amount and the rainfall erosivity


Annual average P (mm)lt15001500ndash2000 2000ndash2500 2500ndash3000 3000ndash3500 3500ndash4000 gt4000

(a)

Annual average R (MJ mmha h yr)lt2000020000ndash30000 30000ndash40000 40000ndash50000 50000ndash60000 60000ndash70000 gt70000

(b)

Figure 4 (a) Annual precipitation and (b) annual rainfall erosivity maps in southern Taiwan Note that isohyet and isoerodent intervals are500mm and 10000MJmmhaminus1 hminus1 yrminus1 respectively

Comparing the four intervals it is seen that the strongestcorrelation exists between the monthly rainfall amount andthe monthly rainfall erosivity

Table 2 shows the mean minimum maximum andCV values of the annual rainfall amount and annual rain-fall erosivity at each of the 55 rainfall stations over theconsidered time period (2002sim2011) From inspection theaverage annual mean rainfall over the 55 stations is equalto 2237mm Moreover the minimum annual rainfall of491mm was recorded at the SyuHai station in 2002 whilethe maximum annual rainfall of 6224mm was recordedat the YuYouShan station in 2005 The annual meanrainfall erosivity over all 55 rainfall stations is equal to31118MJmmhaminus1 hminus1 yrminus1 In addition theminimum rainfallerosivity of 2271MJmmhaminus1 hminus1 yrminus1 was measured at theDanMenShan station in 2002 while the maximum rainfallerosivity of 142370MJmmhaminus1 hminus1 yrminus1 was measured at theYuYouShan station in 2005

An inspection of Table 2 shows that the correlationcoefficients (1199032) between the mean annual rainfall and therainfall erosivity range from 029 to 095 Moreover 49 ofthe 55 stations have a correlation coefficient (1199032) greaterthan 05 which are satisfied by a significance test (two-tailedtest) with a 99 confidence level (119875 value lt 001) The CVvalues of the annual rainfall range from 016 to 049 whilethose of the annual rainfall erosivity range from 016 to 119

Of all the stations the GuTingKeng station has the highestCV (049) for the annual rainfall while theMaoBiTou stationhas the highest CV (119) for the annual rainfall erosivity

GIS (Geographic Information System) was used to inter-polate and plot the spatial variability of the annual rainfallerosivity factor (119877

119910) over the study area using the Kriging

interpolation method [16] Figures 4(a) and 4(b) show theresults obtained for the annual rainfall and annual erosivityrespectively An inspection of Figure 4(a) shows that themean annual total rainfall ranges from 1376 to 4070mmyrminus1Based on the regression relationship for the annual rainfall(119877119910= 274119875120

119910) the rainfall gradient values range from

14785 to 72039 MJ mm haminus1 hminus1 yrminus1 Moreover the Kriginginterpolation results show that the annual rainfall erosivityhas a west-east gradient with values ranging from 15000 to70000MJmmhaminus1 hminus1 yrminus1 It is seen that the spatial distri-butions of the annual rainfall and annual rainfall erosivityrespectively are similar Different interpolationmethodsmayresult in different spatial distributions of the rainfall erosivityHowever Angulo-Martınez and Beguerıa [33] found that allcommon interpolation methods are capable of capturing theregional distribution of the119877 factor given the use of a spatiallydense rainfall database with a high temporal resolution

The rainfall erosivity map presented in Figure 4(b) is ofgreat relevance for soil erosion evaluation and control Ithas implications not only for agriculture but also for many


Table 2 Annual rainfall and annual rainfall erosivity data (2002sim2011) for 55 rainfall stations in southern Taiwan

Number Rainfall station Annual rainfall (mm) Annual rainfall erosivity (MJmmhaminus1 hminus1 yrminus1) Regression models 1199032

Max Min Mean CV Max Min Mean CV1 ZuoYing 2373 700 1602 035 33723 7937 22454 035 119877

119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued


Max Min Mean CV Max Min Mean CV47 FongGang 1972 849 1534 027 37847 5489 17706 049 119877

119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052

activities related to land use planning Furthermore it can beused as a guide for soil conservation practices and landscapemodeling since the 119877 factor is usually an important part oferosion models such as the USLE [16]

The higher erosivity observed in the tropic region iscaused by the high amount of precipitation intensity andkinetic energy of rain The main generating mechanism ofrainfall is convection effect in most tropical regions As aresult the regions receive more rain with higher intensi-ties than the temperate regions dominated by midlatitudecyclones [41]

The regression models to estimate rainfall erosivity forspecific locations are unable to accurately predict actualrainfall erosivity for other locations due to site-specificconditions Therefore simplified methods based on annualprecipitation for estimating rainfall erosivity should be usedwith caution according to location or time period Theirresults deserve careful attention as applying simplified meth-ods to estimating annual rainfall erosivity

32 Applicability of Three Regression Models The applica-bility of the daily monthly and annual regression modelsdeveloped in the previous subsection (ie 119877

119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120

119910 resp) was evaluated

by comparing the results obtained from each model for therainfall erosivity factor with the observed rainfall erosivityfactor computed using the method presented by Wischmeierand Smith [7] Table 3 presents the RMSE andMAPE analysisresults for the estimated and observed rainfall erosivityvalues It is seen that when estimating the 119877

119910factor using

(3) based on the daily rainfall data the MAPE ranges from2 to 49 (CV = 050) and the RMSE varies from 1031to 16350MJmmhaminus1 hminus1 yrminus1 (CV = 055) Similarly whenestimating the 119877

119910factor using the monthly rainfall data the

MAPE ranges from 1 to 37 (CV = 087) while the RMSEvaries from 190 to 17345MJmmhaminus1 hminus1 yrminus1 (CV = 096)Finally when estimating the 119877

119910factor based on the annual

rainfall data the MAPE ranges from 2 to 30 (CV = 059)and the RMSE varies from 454 to 16030MJmmhaminus1 hminus1 yrminus1(CV = 085) Overall it can be seen that the estimation errorsof the three models range from 11 to 49 For the daily

model the error rate exceeds 10 at 11 of the 55 stationsHowever for the monthly and annual regression models theerror rate is less than 10 for 34 and 24 of the 55 stationsrespectively

Figure 5 presents scatter plots showing the relationshipbetween the 119877

119910factors estimated at the 55 stations using

the three regression models and the observed 119877119910factors

computed using the method proposed by Wischmeier andSmith (1978) Note that in the figures presented on theleft the 119909-axis represents the observed annual mean rainfallerosivity factor while the 119910-axis represents the estimatedannual mean 119877

119910factor Furthermore the individual data

points indicate the annual average rainfall erosivity at thedifferent rainfall stations The three figures presented on theright of Figure 5 show the residual distribution as a functionof the annual rainfall erosivity for each of the three modelsHowever that of the daily regression model deviates fartherfrom the normal line in Figure 5(a) Figures 5(b) and 5(c)show that a better agreement exists between the estimatedand observed values of the rainfall erosivity when using themonthly and annual regression models respectively Overallthe results presented in Figure 5 show that in terms ofthe error rate the three regression models can be rankedas follows daily gt annual gt monthly In other words theregression models based on annual and monthly rainfall dataare more accurate than that based on daily rainfall data

According to Table 3 and Figure 5 the data of estimatedannual mean rainfall erosivity was underestimated by dailyrainfall models respectively Nevertheless Liu et al [50] indi-cated that much precipitation information could be providedby daily rainfall data rather than monthly and annual onesDifferent from the results of [50] in China the rainfall eventin southern Taiwan might be consistent for several daysand an underestimate could be therefore produced as dailyrainfall data was used to estimate erosivity

33 Spatial Distribution Comparison of Three RegressionModels Figure 6 presents the annual rainfall erosivity (119877

119910)

and MAPE maps for each of the three regression modelsNote that the observed annual rainfall erosivity map isalso presented for comparison purposes The annual rainfallerosivity (119877

119910) map was based on annual average rainfall


0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 20000 40000 60000 80000 100000Observed rainfall erosivity (MJ mm haminus1 hminus1 yrminus1)

Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()

Estimated rainfall erosivity (MJ mm haminus1 hminus1 yrminus1)

(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)

Figure 5 Validation results for (a) daily (b) monthly and (c) annual regression models based on relationship between estimated 119877119910and

observed 119877119910


Annual average R

lt2000020000ndash30000 30000ndash40000 40000ndash50000 50000ndash60000 60000ndash70000 gt70000

S

N

W EWW

(MJ mmha h yr)

(a)

lt1010ndash1515ndash20 20ndash2525ndash30

35ndash4040ndash45

30ndash35

gt45

MAPElowast ()Annual average R(MJ mmha h yr)

lt2000020000ndash30000 30000ndash40000 40000ndash50000 50000ndash60000 gt60000

ylowast

(b)

lt1010ndash1515ndash20 20ndash2525ndash3030ndash35gt35

MAPElowastlowast ()Annual average R(MJ mmha h yr)


ylowastlowast

(c)

lt1010ndash1515ndash20 20ndash2525ndash30gt30

MAPElowastlowastlowast ()Annual average R(MJ mmha h yr)

lt2000020000ndash30000 30000ndash40000 40000ndash50000 gt50000

ylowastlowastlowast

(d)

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


Table 3 Comparison of estimated rainfall erosivity factor 119877119910and observed rainfall erosivity factor 119877

119910(unit MJmmhaminus1 hminus1 yrminus1)

Rainfall station 119877119910

119877119910

lowast119877119910

lowastlowast119877119910

lowastlowastlowast RMSElowast RMSElowastlowast RMSElowastlowastlowast MAPElowast MAPElowastlowast MAPElowastlowastlowast

ZuoYing 22454 26889 18927 19208 4435 3527 3246 20 16 14FongSen 22072 25814 16576 19409 3742 5496 2663 17 25 12SaYe 23135 27360 20807 19680 4225 2328 3455 18 10 15GangShan 20975 19239 18767 19412 1736 2208 1563 8 11 7GuTingKeng 17198 25627 20154 16625 8429 2956 573 49 17 3MuJha 23355 32082 22104 25164 8727 1251 1809 37 5 8CiShan 24545 27016 26060 24999 2471 1515 454 10 6 2FongSyong 25122 33138 22358 21677 8016 2764 3445 32 11 14Jiashian 41555 50785 40394 35132 9230 1161 6423 22 3 15SiBu 27468 37029 25515 23613 9561 1953 3855 35 7 14FongShan 24753 30880 22707 21887 6127 2046 2866 25 8 12DaLiao 22962 29446 21045 20955 6484 1917 2007 28 8 9YueMei 25374 35168 31863 29181 9794 6489 3807 39 26 15MeiNong 31859 43738 30787 28519 11879 1072 3340 37 3 10JiDong 32550 38068 29408 28979 5518 3142 3571 17 10 11JhuZihJiao 24302 21529 23043 22071 2773 1259 2231 11 5 9JianShan 26262 32897 27935 22429 6635 1673 3833 25 6 15SinFa 47935 42159 48644 41295 5776 709 6640 12 1 14DaJin 40181 47608 39683 36092 7427 498 4089 18 1 10YuYouShan 72039 63584 74076 58778 8455 2037 13261 12 3 18GaoJhong 40858 42227 43422 37294 1369 2564 3564 3 6 9FuSing 33084 32053 34319 30836 1031 1235 2248 3 4 7SiaoGuanShan 41586 37535 47868 40691 4051 6282 895 10 15 2SiNan 46899 48164 64244 53285 1265 17345 6386 3 37 14MeiShan 33285 31932 38104 34153 1353 4819 868 4 14 3NanTienChih 44225 45067 43594 41766 842 631 2459 2 1 6PaiYun 50065 33522 34348 35002 16543 15717 15063 33 31 30NanSi 24998 29183 28933 32542 4185 3935 7544 17 16 30Ali 35257 30350 39240 36458 4907 3983 1201 14 11 3MaJia 64926 48576 60070 48896 16350 4856 16030 25 7 25LiGang 27605 23403 27095 25301 4202 510 2304 15 2 8PingTung 32927 40740 28894 26936 7813 4033 5991 24 12 18SinWei 36733 41425 31463 28437 4692 5270 8296 13 14 23LinLuo 32012 37356 30299 28563 5344 1713 3449 17 5 11NaJhou 20852 25828 19294 19137 4976 1558 1715 24 7 8ChaoJhou 27321 17221 24589 22796 10100 2732 4525 37 10 17FangLiao 16425 13834 16895 15745 2591 470 680 16 3 4MaoBiTou 22740 19711 23591 21800 3029 851 9401 13 4 4JyuCheng 23929 16625 16332 19319 7304 7597 4610 31 32 19LaiYi 43166 33328 35225 31933 9838 7941 11233 23 18 26ChiShan 41204 50232 42742 34806 9028 1538 6398 22 4 16SanDiMan 42442 52468 37553 33943 10026 4889 8499 24 12 20LongCyuan 34742 28349 33969 31908 6393 773 2834 18 2 8LiLi 26451 20600 25869 24221 5851 582 2230 22 2 8ChunMi 19299 25072 20443 20280 5773 1144 981 30 6 5FangShan 20485 22368 18648 19564 1883 1837 921 9 9 4FongGang 17706 21686 17516 18225 3980 190 519 22 1 3ShangDeWun 54945 53340 53694 46476 1605 1251 8469 3 2 15GuSia 35280 26490 35055 34041 8790 225 1239 25 1 4WeiLiaoShan 61679 64075 61211 49864 2396 468 11815 4 1 19


Table 3 Continued


119877119910

lowast 119877119910

lowastlowast 119877119910


SyuHai 28585 23858 24509 27186 4727 4076 1399 17 14 5MouDan 22589 21230 27870 26842 1359 5281 4253 6 23 19MouDanChihShan 24154 21203 26077 29144 2951 1923 4990 12 8 21DanMenShan 16433 12021 16171 17130 4412 262 697 27 2 4ShouKa 24854 31692 28602 28691 6838 3748 3837 28 15 15Max 72039 64075 74076 58778 16543 17345 16030 49 37 30Min 16425 12021 16171 15745 842 190 454 2 1 2Mean 32106 32960 31611 29242 5804 3059 4222 19 10 12CV 039 036 041 034 061 107 087 056 087 059lowastEstimated annual mean 119877 factor using daily rainfall model (119877119889 = 05119875

166

119889)

lowastlowastEstimated annual mean 119877 factor using monthly rainfall model (119877119898 = 06119875149

119898)

lowastlowastlowastEstimated annual mean 119877 factor using annual rainfall model (119877119910 = 274119875120

119910)

erosivity recorded at the 55 rainfall stations and it leads tothe comparison between spatial distribution of the annualrainfall amount and the geographic distribution of annualrainfall erosivity It is seen that the spatial distributions of theestimated and observed values of 119877

119910are similar However

for each regression model the estimated value of 119877119910is

slightly lower than the observed value due to statistical errorsIn addition a comparison of Figures 6(b)sim6(d) confirmsthat the monthly rainfall model yields a better estimationperformance than the daily or annual model

4 Conclusions

The rainfall erosivity factor (119877) is one of the key factors inthe USLE model and has gained increasing importance asthe environmental effects of climate change have becomemore severe This study has proposed three models forestimating the value of 119877 based on daily monthly and annualprecipitation data of rainfall station network respectivelyThe validity of the three models has been evaluated using therainfall data collected over a period of ten yrs (2002sim2011)at 55 rainfall stations in southern Taiwan The results haveshown that of the three models the annual and monthlymodels yield a better agreement with the observed rainfallerosivity factor than the daily model

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to thank the financial support pro-vided by the National Science Council in Taiwan (NSC 102-2625-M-020-002)

References

[1] W H Wischmeier and D D Smith ldquoRainfall energy andits relationship to soil lossrdquo Transactions American GeophysicsUnion vol 39 pp 285ndash229 1958

[2] K G Renard and J R Freimund ldquoUsing monthly precipitationdata to estimate the R-factor in the revised USLErdquo Journal ofHydrology vol 157 no 1ndash4 pp 287ndash306 1994

[3] A M Da Silva ldquoRainfall erosivity map for Brazilrdquo Catena vol57 no 3 pp 251ndash259 2004

[4] R P C Morgan Soil Erosion and Conservation LongmanHarlow Essex UK 1986

[5] N de Santos Loureiroa and M de Azevedo Coutinho ldquoRainfallchanges and rainfall erosivity increase in the Algarve (Portu-gal)rdquo Catena vol 24 no 1 pp 55ndash67 1995

[6] P I A Kinnell ldquoConverting USLE soil erodibilities for use withthe 119876

119877EI30indexrdquo Soil amp Tillage Research vol 45 no 3-4 pp

349ndash357 1998[7] W H Wischmeier and D D Smith Predicting Rainfall Erosion

Losses-Aguide to Conservation Planning Agricultural Hand-book No282 US Department of Agriculture WashingtonDC USA 1978

[8] J O Laws and D A Parsons ldquoThe relation of raindrop size tointensityrdquo Transactions of the American Geophysical Union vol26 pp 452ndash460 1943

[9] A N Sharpley and J R Williams EPICmdashErosionProductivityImpact Calculator U S Department of Agriculture TechnicalBulletin 1990

[10] B Yu and C J Rosewell ldquoAn assessment of a daily rainfallerosivity model for New SouthWalesrdquoAustralian Journal of SoilResearch vol 34 no 1 pp 139ndash152 1996

[11] E A Mikhailova R B Bryant S J Schwager and S D SmithldquoPredicting rainfall erosivity in Hondurasrdquo Soil Science Societyof America Journal vol 61 no 1 pp 273ndash279 1997

[12] B Yu ldquoRainfall erosivity and its estimation for Australiarsquostropicsrdquo Australian Journal of Soil Research vol 36 no 1 pp143ndash165 1998

[13] Q Hu C J Gantzer P-K Jung and B-L Lee ldquoRainfallerosivity in the Republic of Koreardquo Journal of Soil and WaterConservation vol 55 no 2 pp 115ndash120 2000

[14] N de Santos Loureiro and M de Azevedo Coutinho ldquoA newprocedure to estimate the RUSLE EI

30index based on monthly

rainfall data and applied to the Algarve region PortugalrdquoJournal of Hydrology vol 250 no 1ndash4 pp 12ndash18 2001

[15] B Yu G M Hashim and Z Eusof ldquoEstimating the R-factor with limited rainfall data a case study from peninsularMalaysiardquo Journal of Soil andWater Conservation vol 56 no 2pp 101ndash105 2001


[16] C A Bonilla and K L Vidal ldquoRainfall erosivity in CentralChilerdquo Journal of Hydrology vol 410 no 1-2 pp 126ndash133 2011

[17] J-H Lee and J-H Heo ldquoEvaluation of estimation methodsfor rainfall erosivity based on annual precipitation in KoreardquoJournal of Hydrology vol 409 no 1-2 pp 30ndash48 2011

[18] M A Stocking and H A Elwell ldquoRainfall erosivity overRhodesiardquo Transactions of the Institute of British Geographersvol 1 no 2 pp 231ndash245 1976

[19] E Roose ldquoApplication of the universal soil loss equation inWestAfricardquo in Soil Conservation and Management in the HumidTropics D J Greenland andR Lal Eds pp 177ndash188 JohnWileyamp Sons Chichester UK 1977

[20] A Lo S A EI-Swaify E W Dangler and L ShinshiroldquoEffectiveness of EI

30as an erosivity index in Hawaiirdquo in Soil

Erosion and Conservation S A EI-Swaify W C Moldenhauerand A Lo Eds pp 384ndash339 Soil Conservation Society ofAmerica Ankeny Iowa USA 1985

[21] G Balamurugan ldquoSediment balance and delivery in a humidtropical urban river basin the Kelang River Malaysiardquo Catenavol 18 no 3-4 pp 271ndash287 1991

[22] K Banasik and D Gorski ldquoRainfall erosivity for South-EastPolandrdquo in Conserving Soil Resources European Perspectives RJ Rickson Ed Lectures in Soil Erosion Control pp 201ndash207Silsoe College Cranfield University Cranfield UK 1994

[23] E Bergsma P Charman F Gibbons H Humi W C Mold-enhauer and S Panichapong Terminology for Soil Erosionand Conservation International Society of Soil Science (ISSS)Wageningen The Netherlands 1996

[24] A A Millward and J E Mersey ldquoAdapting the RUSLE to modelsoil erosion potential in a mountainous tropical watershedrdquoCatena vol 38 no 2 pp 109ndash129 1999

[25] C-Y Lin W-T Lin and W-C Chou ldquoSoil erosion predictionand sediment yield estimation the Taiwan experiencerdquo Soil andTillage Research vol 68 no 2 pp 143ndash152 2002

[26] D Yang S Kanae T Oki T Koike and K Musiake ldquoGlobalpotential soil erosion with reference to land use and climatechangesrdquo Hydrological Processes vol 17 no 14 pp 2913ndash29282003

[27] S Sudhishri and U S Patnaik ldquoErosion index analysis forEastern Ghat High Zone of Orissardquo Indian Journal of DrylandAgricultural Research and Development vol 19 pp 42ndash47 2004

[28] A R Sepaskhah and P Sarkhosh ldquoEstimating storm erosionindex in southern region of I R Iranrdquo Iranian Journal of Scienceand Technology Transaction B Engineering vol 29 no 3 pp357ndash363 2005

[29] G-H Zhang M A Nearing and B-Y Liu ldquoPotential effectsof climate change on rainfall erosivity in the Yellow River basinof Chinardquo Transactions of the American Society of AgriculturalEngineers vol 48 no 2 pp 511ndash517 2005

[30] D Torri L Borselli F Guzzetti et al ldquoSoil erosion in Italy anoverviewrdquo in Soil Erosion in Europe J Boardman and J PoesenEds pp 245ndash261 John Wiley amp Sons Chichester UK 2006

[31] O Lawal G Thomas and N Babatunde ldquoEstimation ofpotential soil losses on a regional scale a case of Abomey-Bohicon regionrdquo Benin Republic Agricultural Journal vol 2 no1 pp 1ndash8 2007

[32] J J le Roux T L Morgenthal J Malherbe D J Pretorius andP D Sumner ldquoWater erosion prediction at a national scale forSouth AfricardquoWater SA vol 34 no 3 pp 305ndash314 2008

[33] M Angulo-Martınez and S Beguerıa ldquoEstimating rainfallerosivity from daily precipitation records a comparison amongmethods using data from the Ebro Basin (NE Spain)rdquo Journal ofHydrology vol 379 no 1-2 pp 111ndash121 2009

[34] Z Xin X Yu Q Li and X X Lu ldquoSpatiotemporal variation inrainfall erosivity on theChinese Loess Plateau during the period1956ndash2008rdquo Regional Environmental Change vol 11 no 1 pp149ndash159 2011

[35] N Diodata ldquoEstimating RUSLErsquos rainfall factor in the partof Italy with a Mediterranean rainfall regimerdquo Hydrology andEarth System Sciences vol 8 no 1 pp 103ndash107 2004

[36] S Grauso N Diodato and V Verrubbi ldquoCalibrating a rainfallerosivity assessment model at regional scale in Mediterraneanareardquo Environmental Earth Sciences vol 60 no 8 pp 1597ndash1606 2010

[37] C W Richardson G R Foster and D A Wright ldquoEstimationof erosion index from daily rainfall amountrdquo TransactionsAmerican Society of Agricultural Engineers vol 26 no 1 pp 153ndash157 1983

[38] H Elsenbeer D K Cassel and W Tinner ldquoA daily rainfallerosivity model for western Amazoniardquo Journal of Soil ampWaterConservation vol 48 no 5 pp 439ndash444 1993

[39] D Capolongo N Diodato C M Mannaerts M Piccarretaand R O Strobl ldquoAnalyzing temporal changes in climateerosivity using a simplified rainfall erosivity model in Basilicata(Southern Italy)rdquo Journal of Hydrology vol 356 no 1-2 pp 119ndash130 2008

[40] V Bagarello and F DrsquoAsaro ldquoEstimating single storm erosionindexrdquo Transactions of the American Society of AgriculturalEngineers vol 37 no 3 pp 785ndash791 1994

[41] G Petkovsek andMMikos ldquoEstimating the R factor from dailyrainfall data in the sub-Mediterranean climate of southwestSloveniardquo Hydrological Sciences Journal vol 49 no 5 pp 869ndash877 2004

[42] B Yu and C J Rosewell ldquoA robust estimator of the R-factor forthe universal soil loss equationrdquo Transactions of the AmericanSociety of Agricultural Engineers vol 39 no 2 pp 559ndash561 1996

[43] S D Angima D E Stott M K OrsquoNeill C K Ong andG A Weesies ldquoSoil erosion prediction using RUSLE forcentral Kenyan highland conditionsrdquo Agriculture Ecosystemsand Environment vol 97 no 1ndash3 pp 295ndash308 2003

[44] F K Salako ldquoDevelopment of isoerodentmaps for Nigeria fromdaily rainfall amountrdquoGeoderma vol 156 no 3-4 pp 372ndash3782010

[45] N Diodato ldquoPredicting RUSLE (Revised Universal Soil LossEquation) monthly erosivity index from readily available rain-fall data inMediterranean areardquo Environmentalist vol 26 no 1pp 63ndash70 2006

[46] N Diodato and G Bellocchi ldquoEstimating monthly (R)USLEclimate input in a Mediterranean region using limited datardquoJournal of Hydrology vol 345 no 3-4 pp 224ndash236 2007

[47] J S Selker D A Haith and J E Reynolds ldquoCalibration andtesting of a daily rainfall erosivity modelrdquo Transactions of theAmerican Society of Agricultural Engineers vol 33 no 5 pp1612ndash1618 1990

[48] N Diodato M Ceccarelli and G Bellocchi ldquoDecadal andcentury-long changes in the reconstruction of erosive rainfallanomalies in a Mediterranean fluvial basinrdquo Earth SurfaceProcesses and Landforms vol 33 no 13 pp 2078ndash2093 2008


[49] J M V d Knijff R J A Jones and L Montanarella ldquoSoilerosion risk assessment in Italyrdquo European Soil Bureau EUR19044 EN 1999

[50] Z Liu C Colin A Trentesaux et al ldquoLate Quaternary climaticcontrol on erosion and weathering in the eastern TibetanPlateau and the Mekong Basinrdquo Quaternary Research vol 63no 3 pp 316ndash328 2005

International Journal of

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation



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of rainfall events respectively Summing the rainfall erosivityindex of all the rainfall events over one year the annualrainfall erosivity index can be obtained as

119877119910=

119884

sum119895=1

119877119895 (3)

where 119884 is the number of rainfall events in the year Inaddition the unitary kinetic energy 119890

119894is deduced from the

relationship between the raindrop diameter and the rainfallintensity as follows [8]

119864119894=

0119 + 00873 log 119868119894

for 119868119894lt 76mmhr

0283 for 119868119894ge 76mmhr

(4)

The rainfall erosivity index 119877 has been widely testedand applied in many countries and regions around the worldwhose rainfall intensity is characterized mainly as moderateto high [9ndash15] In computing the rainfall erosivity factorthe maximum 30-min rainfall intensities for the storm andheavy storm events are generally computed on the basis ofhyetograph data or high-resolution rainfall data (pluviographdata) Generally speaking pluviograph data for at least 20 yrsare required to compute the rainfall erosivity for a given studyarea using the (119877) USLE formulation [2] However such largevolumes of data are not available for all regions of the worldFurthermore even if sufficient pluviograph data are availablecomputing the rainfall erosivity is a complicated and tedioustask To overcome this problem various simplified modelshave been proposed for estimating the rainfall erosivity factorusing more readily available precipitation data

Among suchmodels those based on annual precipitationdata are particularly common since annual rainfall data areavailable in most regions of the world and tend to be fairlyreliable Furthermore various studies have shown that a goodcorrelation exists between the annual rainfall erosivity andthe annual precipitation amount at many locations aroundtheworld [16 17] Accordingly annual precipitation data havebeen used to obtain simple estimates of the rainfall erosivityin many countries [2 11 18ndash34]

Several researchers have used both annual precipitationdata and maximum daily and hourly precipitation data toestimate the rainfall erosivity factor in the Mediterraneanregion [35 36] However the models used in these studiesestimate the mean annual rainfall erosivity over severalyrs rather than the rainfall erosivity in a particular yrMany regression models based on variations in the observedrainfall erosivity or seasonal erosivity have been proposedfor predicting the daily rainfall erosivity [15 33 37ndash44] ormonthly rainfall erosivity [45 46] It has been shown thatthe use of daily or monthly rainfall records provides a betterunderstanding of the rainfall erosivity of individual stormsthan annual precipitation data [34] In constructing daily ormonthly prediction models it is necessary to compute therainfall erosivity on a daily or monthly basis respectivelyHowever calculating the daily and monthly rainfall erosivityis more challenging than computing that for a particularstorm For example if it rains from May 31 to June 1

the observed rainfall erosivity for this storm has just onevalue However the corresponding data should be dividedinto two different values (ie daily or monthly segments)when constructing daily ormonthlymodelsThus the annualsum of the reclassified rainfall erosivity is different from theobserved value due to the use of different boundary con-ditions Moreover the daily or monthly rainfall parametersused in daily and monthly models respectively provide aninadequate description of the kinetic energy and rainfallintensity terms in the rainfall erosivity index [33 47]

Although annual regression models are a gross oversim-plification of the observed variation in the rainfall erosivityand their estimated values are rough [33 48] they never-theless represent a viable alternative to detailed quantitativeassessments in providing a long-term assessment of theannual mean rainfall erosivity using the USLE formulation[49] Thus as discussed above numerous researchers haveproposed methods for estimating the rainfall erosivity basedon annual precipitation data andor other rainfall parametersHowever such models require careful optimization andcalibration for each specific location and include site-specificcoefficients The proposed study is to find out the suitablemodels among daily monthly and annual precipitation data

The present study proposes three regression models forestimating the rainfall erosivity and finding out the suitablemodels in southern Taiwan based on daily monthly andannual precipitation data of rainfall station network respec-tively even without 30-min rainfall dataThe detailed goals ofthis study can be summarized as follows (a) to construct newmodels for the large-scale estimation of the erosivity factor insouthern Taiwan and (b) to analyze the spatial distribution ofthe daily monthly and annual rainfall erosivity in southernTaiwan

2 Materials and Methods

21 Study Area This study considered the regions of Kaohsi-ung City and Pingtung County in southern Taiwan The tworegions cover areas of 2961 km2 and 2784 km2 respectivelyand contain a total of 55 rainfall stations (see Figure 1) Bothregions commonly experience extreme rainfall events duringthe summer months For example in August 2009 TyphoonMorakot resulted in catastrophic damage that left 665 peopledead 34 others missing and roughly US$ 44 billion indamages

22 Rainfall Data Table 1 summarizes the basic geographicand rainfall data of the 28 rainfall stations in Kaohsiung Cityand 27 rainfall stations in Pingtung County over the 10 yrperiod extending from 2002 to 2011 Traditionally the high-resolution rainfall data recorded by each station in Table 1 areused to calculate the rainfall erosivity factor in accordancewith (2)ndash(4) [7] In the present study the reliability of thesedata was evaluated using the 10-min rainfall data obtainedfor the corresponding period from the Central WeatherBureau (CWB) of Taiwan In the present study 16560 stormevents were selected from the 550 observed annual rainfalldatasets presented in Table 1 (ie 55 stations times 10 yrs) Thecorresponding daily monthly and annual rainfall data were






Table 1 Continued



Total 550 16560

120∘E 121∘E

235∘N

230∘N

225∘N

220∘N

Kaohsiung City

Pingtung County


0 12500 25000 50000

(m)

S

N

W E









(Kriging)


(Rj)

Pj ge 127mm

(n = 2266)


Observed Ry

Rd = aPbd Rm = aPb

m Ry = aPby

Rlowasty =

Y

sumj=1

Rd =Y

sumj=1

aPbd Rlowastlowast

y =Y

sumj=1

Rm =Y

sumj=1


y =Y

sumj=1

Ry =Y

sumj=1

aPby

Ry =Y

sumj=1

Rj

Ry =Y

sumj=1

RjRd =D

sumj=1

Rj Rm =M

sumj=1

Rj





MAPE =100381610038161003816100381610038161003816100381610038161003816


119877obe

100381610038161003816100381610038161003816100381610038161003816times 100 ()

(5)









CV = 120590119906 (6)






0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

N = 16560


154 (r2 = 080)

Pj (mm)

Rj

(MJ m

mh

a h)

(a)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 200 400 600 800 1000 1200

N = 3616


166 (r2 = 082)

Pd (mm)

Rd

(MJ m

mh

a h)

(b)

0

20000

40000

60000

80000

100000

120000

0 500 1000 1500 2000 2500 3000 3500

N = 1413



149 (r2 = 091)

Pm (mm)

Rm

(MJ m

mh

a h)

(c)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 2000 4000 6000 8000

N = 550


120 (r2 = 073)

Py (mm)

Ry

(MJ m

mh

a h yr

)

(d)








erosivity (119877119910)




(119877119895= 073119875154





119889 1199032 = 082)




119898) and



119898= 060119875149

119898 1199032 = 091

and 119877119910= 274119875120





(a)


(b)
















119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Table 1 Continued



Total 550 16560

120∘E 121∘E

235∘N

230∘N

225∘N

220∘N

Kaohsiung City

Pingtung County


0 12500 25000 50000

(m)

S

N

W E









(Kriging)


(Rj)

Pj ge 127mm

(n = 2266)


Observed Ry

Rd = aPbd Rm = aPb

m Ry = aPby

Rlowasty =

Y

sumj=1

Rd =Y

sumj=1

aPbd Rlowastlowast

y =Y

sumj=1

Rm =Y

sumj=1


y =Y

sumj=1

Ry =Y

sumj=1

aPby

Ry =Y

sumj=1

Rj

Ry =Y

sumj=1

RjRd =D

sumj=1

Rj Rm =M

sumj=1

Rj





MAPE =100381610038161003816100381610038161003816100381610038161003816


119877obe

100381610038161003816100381610038161003816100381610038161003816times 100 ()

(5)









CV = 120590119906 (6)






0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

N = 16560


154 (r2 = 080)

Pj (mm)

Rj

(MJ m

mh

a h)

(a)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 200 400 600 800 1000 1200

N = 3616


166 (r2 = 082)

Pd (mm)

Rd

(MJ m

mh

a h)

(b)

0

20000

40000

60000

80000

100000

120000

0 500 1000 1500 2000 2500 3000 3500

N = 1413



149 (r2 = 091)

Pm (mm)

Rm

(MJ m

mh

a h)

(c)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 2000 4000 6000 8000

N = 550


120 (r2 = 073)

Py (mm)

Ry

(MJ m

mh

a h yr

)

(d)








erosivity (119877119910)




(119877119895= 073119875154





119889 1199032 = 082)




119898) and



119898= 060119875149

119898 1199032 = 091

and 119877119910= 274119875120





(a)


(b)
















119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















(Kriging)


(Rj)

Pj ge 127mm

(n = 2266)


Observed Ry

Rd = aPbd Rm = aPb

m Ry = aPby

Rlowasty =

Y

sumj=1

Rd =Y

sumj=1

aPbd Rlowastlowast

y =Y

sumj=1

Rm =Y

sumj=1


y =Y

sumj=1

Ry =Y

sumj=1

aPby

Ry =Y

sumj=1

Rj

Ry =Y

sumj=1

RjRd =D

sumj=1

Rj Rm =M

sumj=1

Rj





MAPE =100381610038161003816100381610038161003816100381610038161003816


119877obe

100381610038161003816100381610038161003816100381610038161003816times 100 ()

(5)









CV = 120590119906 (6)






0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

N = 16560


154 (r2 = 080)

Pj (mm)

Rj

(MJ m

mh

a h)

(a)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 200 400 600 800 1000 1200

N = 3616


166 (r2 = 082)

Pd (mm)

Rd

(MJ m

mh

a h)

(b)

0

20000

40000

60000

80000

100000

120000

0 500 1000 1500 2000 2500 3000 3500

N = 1413



149 (r2 = 091)

Pm (mm)

Rm

(MJ m

mh

a h)

(c)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 2000 4000 6000 8000

N = 550


120 (r2 = 073)

Py (mm)

Ry

(MJ m

mh

a h yr

)

(d)








erosivity (119877119910)




(119877119895= 073119875154





119889 1199032 = 082)




119898) and



119898= 060119875149

119898 1199032 = 091

and 119877119910= 274119875120





(a)


(b)
















119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

N = 16560


154 (r2 = 080)

Pj (mm)

Rj

(MJ m

mh

a h)

(a)

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 200 400 600 800 1000 1200

N = 3616


166 (r2 = 082)

Pd (mm)

Rd

(MJ m

mh

a h)

(b)

0

20000

40000

60000

80000

100000

120000

0 500 1000 1500 2000 2500 3000 3500

N = 1413



149 (r2 = 091)

Pm (mm)

Rm

(MJ m

mh

a h)

(c)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 2000 4000 6000 8000

N = 550


120 (r2 = 073)

Py (mm)

Ry

(MJ m

mh

a h yr

)

(d)








erosivity (119877119910)




(119877119895= 073119875154





119889 1199032 = 082)




119898) and



119898= 060119875149

119898 1199032 = 091

and 119877119910= 274119875120





(a)


(b)
















119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(a)


(b)
















119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119910= 3347119875088 062

2 FongSen 2253 889 1616 031 39689 7512 22072 043 119877119910= 6647119875078 029

3 SaYe 2373 1306 1736 023 33723 16132 23135 026 119877119910= 090119875136 071

4 GangShan 2671 909 1617 038 46687 8273 20975 061 119877119910= 223119875125 074

5 GuTingKeng 2656 537 1421 049 38869 5033 17198 063 119877119910= 165119875126 095

6 MuJha 4461 1412 2154 043 59574 16691 23355 052 119877119910= 117119875131 093

7 CiShan 3057 1091 1996 035 40927 13247 24545 040 119877119910= 1517119875097 073

8 FongSyong 2814 881 1772 034 41035 10802 25122 042 119877119910= 942119875105 064

9 Jiashian 4461 1506 2650 039 76637 15779 41555 053 119877119910= 310119875120 075

10 SiBu 2981 982 1903 034 49680 10644 27468 050 119877119910= 059119875142 086

11 FongShan 2672 867 1787 033 37336 11659 24753 038 119877119910= 692119875109 077

12 DaLiao 2454 821 1723 031 32686 7103 22962 038 119877119910= 368119875117 066

13 YueMei 3598 1410 2271 028 41677 17889 25374 033 119877119910= 1790119875095 074

14 MeiNong 3399 1083 2227 035 59758 16033 31859 049 119877119910= 562119875112 081

15 JiDong 3221 1171 2257 030 47197 18988 32550 029 119877119910= 68483119875050 030

16 JhuZihJiao 2848 876 1799 036 49183 7989 24302 055 119877119910= 936119875105 053

17 JianShan 3063 632 1823 039 60047 6044 26262 058 119877119910= 127119875132 086

18 SinFa 4589 1630 3032 034 75976 21836 47935 044 119877119910= 447119875115 076

19 DaJin 4105 1322 2710 032 66543 13987 40181 042 119877119910= 095119875134 083

20 YuYouShan 6224 1767 4070 034 142370 19412 72039 050 119877119910= 043119875144 088

21 GaoJhong 4565 1188 2785 040 69908 12387 40858 054 119877119910= 128119875130 072

22 FuSing 4231 1077 2377 046 81114 7355 33084 073 119877119910= 081119875135 065

23 SiaoGuanShan 4164 1697 2995 026 93739 14726 41586 054 119877119910= 016119875155 066

24 SiNan 5557 1800 3750 032 98956 13550 46899 059 119877119910= 150119875125 054

25 MeiShan 4270 1122 2589 039 69331 10799 33285 065 119877119910= 025119875149 077

26 NanTienChih 4986 1615 3661 033 101544 9538 41011 073 119877119910= 002119875174 073

27 PaiYun 3844 1294 2642 032 33848 6862 18175 048 119877119910= 045119875133 079

28 NanSi 3572 1230 2672 033 48871 6949 24998 056 119877119910= 0033119875172 086

29 ALi 4049 1661 2733 034 59940 15606 35257 051 119877119910= 035119875145 086

30 MaJia 5530 1820 3491 035 122022 25807 64926 050 119877119910= 625119875112 064

31 LiGang 3142 1201 2016 032 39945 12491 27605 033 119877119910= 2331119875093 062

32 PingTung 3351 990 2124 034 65988 10229 32927 050 119877119910= 184119875127 076

33 SinWei 3999 1312 2222 037 87155 13318 36733 060 119877119910= 238119875124 064

34 LinLuo 3267 1139 2230 030 53448 17799 32012 034 119877119910= 5192119875083 061

35 NaJhou 2340 773 1597 033 33690 9998 20852 038 119877119910= 4340119875083 054

36 ChaoJhou 2581 811 1848 032 52474 6426 27321 049 119877119910= 097119875135 066

37 FangLiao 2311 534 1376 047 28044 4763 16425 050 119877119910= 867119875103 081

38 MaoBiTou 2050 998 1419 021 99535 10631 22740 119 119877119910= 0002119875219 049

39 JyuCheng 2218 986 1610 026 62730 7558 23929 070 119877119910= 007119875171 064

40 LaiYi 3439 1556 2448 024 82126 21753 43166 047 119877119910= 1017119875106 036

41 ChiShan 3714 1347 2630 028 67586 15140 41204 038 119877119910= 487119875114 061

42 SanDiMan 3773 1655 2575 026 75709 20727 42442 044 119877119910= 127119875132 064

43 LongCyuan 3653 1249 2438 031 65942 12170 34742 044 119877119910= 227119875123 067

44 LiLi 2864 1137 1944 031 39750 12995 26451 038 119877119910= 1746119875096 056

45 ChunMi 2615 847 1677 033 32659 7211 19299 045 119877119910= 182119875124 075

46 FangShan 2281 1074 1627 027 66431 8886 20485 081 119877119910= 017119875156 058


Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 2 Continued



119910= 077119875136 068

48 ShangDeWun 2671 909 1700 033 42345 11248 54945 016 119877119910= 1734119875099 059

49 GuSia 3495 1598 2582 027 48113 16361 35280 032 119877119910= 278119875120 073

50 WeiLiaoShan 5666 1377 3548 040 121787 14042 61679 052 119877119910= 266119875123 087

51 SyuHai 2939 491 2022 037 53235 4231 28585 049 119877119910= 214119875121 088

52 MouDan 2661 1396 2118 020 50943 13706 22589 050 119877119910= 050119875141 056

53 MouDanChihShan 3377 1577 2268 026 53046 13279 24154 052 119877119910= 099119875130 050

54 DanMenShan 2129 558 1457 041 30074 2271 16433 049 119877119910= 1052119875 048

55 ShouKa 2606 1735 2184 016 28325 10158 24854 020 119877119910= 124119875125 052





119889= 050119875166

119889

119877119898= 060119875149

119898 and 119877

119910= 274119875120



119910factor using















119910)




0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(a)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000

Bias

()


(b)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000


Estim

ated

rain

fall

eros

ivity

(MJ m

m h

aminus1

hminus1

yrminus1)

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

50

0 20000 40000 60000 80000 100000Bias

()


(c)


observed 119877119910


Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Annual average R


S

N

W EWW

(MJ mmha h yr)

(a)


35ndash4040ndash45

30ndash35

gt45



ylowast

(b)




ylowastlowast

(c)




ylowastlowastlowast

(d)






119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119877119910

lowast119877119910





Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 3 Continued


119877119910

lowast 119877119910




166

119889)


119898)


119910)





4 Conclusions




Acknowledgment


References





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article evaluation of annual rainfall...

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