HYDROLOGICAL PROCESSESHydrol. Process. (2015)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.10737

Exploring the effect of different time resolutions to calculate therainfall erosivity factor R in Calabria, southern Italy

Paolo Porto*Dipartimento di Agraria, Università degli Studi Mediterranea di Reggio Calabria, Reggio Calabria, Italy

*CdegE-m

Co

Abstract:

The rainfall erosivity factor R of the Universal Soil Loss Equation is a good indicator of the potential of a storm to erode soil, as itquantifies the raindrop impact effect on the soil based on storm intensity. The R-factor is defined as the average annual value ofrainfall erosion index, EI, calculated by cumulating the EI values obtained for individual storms for at least 22 years. Bydefinition, calculation of EI is based on rainfall measurements at short time intervals over which the intensity is essentiallyconstant, i.e. using so-called breakpoint data. Because of the scarcity of breakpoint rainfall data, many authors have useddifferent time resolutions (Δt= 5, 10, 15, 30, and 60min) to deduce EI in different areas of the world. This procedure affects thereal value of EI because it is strongly dependent on Δt. In this contribution, after a general overview of similar studies carried outin different countries, the relationship between EI and Δt is explored in Calabria, southern Italy. The use of 17 139 storm eventscollected from 65 rainfall stations allowed the calculation of EI for different time intervals ranging from 5 to 60min. The overallresults confirm that calculation of EI is dependent on time resolution and a conversion factor able to provide its value for therequired Δt is necessary. Based on these results, a parametric equation that gives EI as a function of Δt is proposed, and a regionalmap of the scale parameter a that represents the conversion factor for converting fixed-interval values of (EI30)Δt to values of(EI30)15 is provided in order to calculate R anywhere in the region using rainfall data of 60min. Copyright © 2015 John Wiley &Sons, Ltd.

KEY WORDS rainfall erosivity; USLE; soil erosion

Received 4 September 2015; Accepted 27 October 2015

INTRODUCTION

In the last few decades, the Universal Soil Loss Equation(USLE) (Wischmeier and Smith, 1978), and its derivedforms RUSLE (Renard et al., 1997), MUSLE (Williamsand Berndt, 1972), and USLE-M (Kinnell and Risse,1998) for predicting soil erosion, have been applied inmany areas of the world (Pimentel, 1993; Boardman andPoesen, 2006) including Italy (Cinnirella et al., 1998; DiStefano et al., 2000; Bagarello et al., 2011). The USLE isthe product of six major numeric factors relating toclimate, soil characteristics, topography, vegetation, andsupport practices. In formula

A ¼ RK LSCP (1)

where R (MJmmha�1 h�1 year�1) is the rainfall erosivityfactor, K (t ha�1 per unit of R) is the soil erodibility factor,L is the slope-length factor, S is the slope-steepness

orrespondence to: Paolo Porto, Dipartimento di Agraria, Universitàli Studi Mediterranea di Reggio Calabria, Reggio Calabria, Italy.ail: paolo.porto@unirc.it

pyright © 2015 John Wiley & Sons, Ltd.

factor, C is the cover and management factor, and P is thesupporting conservation practice factor. The factors L, S,C, and P are dimensionless, and Equation (1) gives thevalue of soil loss A in t ha�1 year�1.Wischmeier (1959) showed that if all the factors other

than R are maintained at constant, the amount of soil lossis directly proportional to the value of the rainfallerosivity factor. The R-factor is in fact a good indicatorof the potential of a storm to erode soil as it combinesboth the raindrop impact effect on the soil and theturbulence of runoff to transport dislodged soil particlesfrom the field (Wischmeier and Smith, 1965). The R-factor is defined as the average annual value of rainfallerosion index, EI, calculated by cumulating the EI valuesobtained for individual storms for at least 22 years(Wischmeier and Smith, 1978).The knowledge of EI for each erosive event is crucial

for applying Equation (1), although its calculation istedious and time consuming as it requires a continuousrecord of rainfall intensity. In fact, the EI index(MJmmha�1 h�1) for a single event is the product oftotal storm energy E (MJ ha�1) and maximum 30-minintensity i30 (mmh�1), viz.

P. PORTO

EI ¼ E i30 ¼ ∑m

j¼1ejΔhj

!i30 (2)

where ej (MJha�1mm�1) indicates the rainfall energy perunit depth of rainfall per unit area and Δhj (mm) is thedepth of rainfall for the jth interval of the stormhyetograph, which is divided into m parts with essentiallyconstant intensity.The rainfall energy ej can be estimated using the

equations proposed by Foster et al. (1981):

ej ¼ 0:119þ 0:0873 log10 ij� �

if ij ≤ 76 mmh�1

(3a)

ej ¼ 0:283 if ij > 76 mmh�1 (3b)

where ij (mmh�1) is the rainfall intensity calculated asfollows:

ij ¼ ΔhjΔtj

(4)

where Δtj is the interval duration over which intensity isassumed to be constant.Equations (3a) and (3b) have been calibrated for

climatic conditions of the USA, but they have beenlargely applied throughout the world, although mucheffort has been made in providing alternative equationsfor calculating ej in the USA (Brown and Foster, 1987) orin other countries (Bolinne et al., 1984; Brandt, 1990;Rosewell, 1986; Zanchi and Torri, 1980; Carollo andFerro, 2015). However, even if it is well known that thechoice of different equations to obtain ej affects theoverall calculation of EI and then the estimate of soil lossby Equation (1), only a few authors have given emphasisto the effect of the rainfall measurement interval incalculating EI (Istok et al., 1986; Williams and Sheridan,1991; Renard et al., 1997; Agnese et al., 2006; Yin et al.,2007; Panagos et al., 2015a, b). A recent study ofDunkerley (2010) clearly shows that the rain rates of sub-event intervals such as the maximum 5- and 15-min rates(I5 or I30) strongly affect the properties of the relatedrainfall event. These results suggest that care must betaken when a time interval is selected to calculate thecorresponding rainfall intensity.By definition, calculation of EI is based on rainfall

measurements at short time intervals over which theintensity is essentially constant, i.e. using so-calledbreakpoint data (Wischmeier and Smith, 1978). Ingeneral, breakpoint data relate to the values read manuallyfrom graphical charts that are generated by continuouslyrecording rain gauges (Yin et al., 2007). These data are

Copyright © 2015 John Wiley & Sons, Ltd.

recorded as pairs of values representing time andcumulative depth of rainfall corresponding to timeintervals where rainfall intensity is assumed constant.This procedure, even if originally suggested byWischmeier and Smith (1978), includes a subjectivechoice in selecting the ‘breaks’ or changes in the rainfallintensity of the storm event. For this reason, different timeresolutions provided by different specific rain gaugesproduce different values of EI. With the development ofautomatic recorders, data are provided at fixed timeintervals, and this caused a different interpretation of‘constant intensity’.In a study carried out in the USA, Istok et al. (1986),

assuming that a 15-min interval was reasonably shortenough to obtain constant intensity rainfall data, exploredan alternative procedure to determine EI using hourlyrainfall measurements. Using data from three sites inwestern Oregon, they showed the sensitivity of the EIestimates to the time resolution of rainfall measurements.In particular, they calculated the energy and intensitycomponents of EI for individual rainstorms using 15 and60-min measurement intervals. The overall resultsshowed that there was a high significant correlationbetween (EI30)15 and (EI30)60 and that the former can becalculated using a simple linear model, viz.

EI30ð Þ15 ¼ a EI30ð Þ60 (5)

where the coefficient a assumed values ranging from1.193 to 1.378.Based on thesefindings, Istok et al. (1986) established that,

as the rainfall measurement interval decreased from 60 to15min, values of EI increased by between 19.3% and 37.8%.The study of Istok et al. (1986), although innovative,

was of course limited, as it explored only three rainfallstations located in a small area in Oregon. Also, aconstant rainfall depth resolution of 0.25mm was used forEI calculation. Following this last assumption, Williamsand Sheridan (1991), using breakpoint rainfall dataavailable for the Coastal Plain Experiment Station inTifton (GA, USA), provided values of the coefficient afor different depth resolutions and for different timeinterval records. Based on their relationships, thecomparison between (EI30)15 and (EI30)60 for a 0.25-mm depth resolution gave a coefficient a = 1.639,substantially higher than that obtained by Istok et al.(1986). The authors explained this result, considering thedifference in I30 for the high-intensity, short-durationrainfall events typical of the southeastern USA.Some years later, an extensive investigation was

conducted in the USA (Renard et al., 1997) aimed atexploring the relationship between (EI30)15 and (EI30)60for larger areas. In that study, 713 stations were selected,and all storms were included in the calculations of EI. The

Hydrol. Process. (2015)

THE RAINFALL EROSIVITY FACTOR R IN CALABRIA

overall results provided values of a ranging from 1.08 to3.16 and confirmed the spatial variability of the regressioncoefficient of Equation (5).The influence of the rainfall measurement interval on

the calculation of EI30 was also investigated in Italy byAgnese et al. (2006). In that paper, 688 erosive eventscollected from seven rainfall stations located in Sicilywere used. Rainfall data, recorded with a temporalresolution Δt=5min, were aggregated at Δt=15 and60min, and the relationship between (EI30)15 and (EI30)60was explored. Although the variation of a was quite low(1.297–1.363), the authors emphasized that Equation (5)must be locally calibrated.More recently, Yin et al. (2007) explored the accuracy

of EI30 estimations based on 5-, 10-, 15-, 30-, and 60-mintime-resolution rainfall measurements as compared withEI30 estimations from breakpoint data. In that study, 456storm events collected from five stations in eastern Chinawere used. Although the analysis focused on a compar-ison with breakpoint data, the slope coefficients listed intheir table III (Yin et al., 2007) allow calculation of theregression coefficient of Equation (5). Based on theirresults, the coefficient a assumes values ranging from1.408 (at Anxi) to 1.722 (at Binxian) and confirmed onceagain its spatial variability.The studies reported earlier clearly suggest that the

time resolution of rainfall measurements is crucial in

Crotone

Catanzaro

Cosenza

ViboValentia

0 50km

ReggioCalabria

Ionian Sea

Tyrrhenian Sea

Gulf of Taranto

IT

AL

Y

200km

CALABRIA

44 Site code (see Table 1)

Site used for calibration

Site used for validation

Figure 1. The study area and the

Copyright © 2015 John Wiley & Sons, Ltd.

determining EI30 because, as the rainfall measurementinterval decreases from 60 to 15min, values of EIincrease in different proportions. However, if detailedinformation on local rainfall is available and a relation-ship between (EI30)15 and (EI30)Δt can be established,rainfall data at larger temporal resolutions, readilyavailable, can be used to calculate EI30 with a certainaccuracy.In the study reported here, rainfall data relating to

17139 erosive events collected from 65 stations locatedin Calabria (Italy) were used to establish a relationshipbetween (EI30)15 and (EI30)Δt. In the analysis, thetemporal dependence and the spatial variation of theregression coefficient of Equation (5) were investigated,and a general relationship of the form of Equation (5) isproposed for the study area.

DATA AND METHODS

The data used in this analysis were obtained from 65rainfall stations located in Calabria, southern Italy(Figure 1). The study sites cover a large area (ca.15 079km2) that includes three different climate zones: asemi-arid zone located along the Ionian coast in theeastern side, a more humid zone located along the westernTyrrhenian coast, and the central zone that includes the

1

4

5

7

29

9

10

11

12

14

15

33

19

25

2

24

26

17

27

28

60

31

35

37

38

42

43

46

4720

52

53

54

45

50

56

16

57

40

58

59

63

51

64

65

3

6

13

8

18

212330

32

34

36

39

41

44

48

55

22

61

6249

2580000 2620000 2660000 2700000

4200000

4250000

4300000

4350000

4400000

65 stations used for the analysis

Hydrol. Process. (2015)

Table I. The main characteristics of the rainfall stations used in the analysis

Code SitePa

(mm)Studyperiod N

Elev(m a.s.l.)

Dist(km)

60min 30min 10min 5min

a r2 a r2 a r2 a r2

1 Acri 1011 1991–2011 378 750 22.7 1.3636 0.9731 1.0384 0.9973 0.9791 0.9991 0.9411 0.99922 Amantea 924 1993–2011 414 54 2 1.6899 0.9433 1.1349 0.9678 0.9700 0.9975 0.9305 0.99693 Antonimina 1379 1992–2003 239 310 8.1 1.2065 0.9784 1.0820 0.9955 0.9645 0.9981 0.9323 0.99924 Ardore Superiore 924 1990–2011 373 250 5.8 1.1760 0.9849 1.0525 0.9979 0.9935 0.9998 0.9800 0.99895 Belvedere 977 2002–2011 262 10 0.6 1.7534 0.9718 1.2349 0.9558 0.9634 0.9988 0.9372 0.99806 Camigliatello 1251 1993–2004 334 1730 31.5 1.3218 0.9474 1.0604 0.9852 0.9772 0.9978 0.9297 0.99767 Capo Spartivento 616 1991–2011 286 48 0.5 1.6628 0.9093 1.0930 0.9873 0.9251 0.9968 0.9045 0.99808 Cassano Jonico 738 2002–2011 172 250 14.6 1.8460 0.9616 1.2596 0.9717 0.9956 0.9975 0.9566 0.99779 Castrovillari 833 1990–2005 251 353 19.8 1.6629 0.9576 1.0932 0.9952 0.9546 0.9991 0.9214 0.999210 Catanzaro 988 1991–2006 323 334 10.3 1.5244 0.9809 1.1446 0.9780 0.9642 0.9984 0.9365 0.998611 Cecita 1086 1990–2005 282 1180 31.1 1.4484 0.9709 1.0515 0.9953 0.9926 0.9983 0.9691 0.994212 Cetraro Superiore 963 1993–2011 372 76 3.1 1.8018 0.9307 1.1453 0.9609 0.9581 0.9966 0.9143 0.994913 Chiaravalle Centrale 1434 1990–2005 321 714 12 1.1307 0.9484 1.0310 0.9946 0.9853 0.9987 0.9709 0.998114 Cirò Marina 716 1991–2003 147 6 2 1.5608 0.9302 1.1437 0.9773 0.9457 0.9958 0.9217 0.996415 Cittanova 1456 1990–2006 420 407 19.1 1.4139 0.9230 1.0636 0.9880 0.9678 0.9965 0.9204 0.996916 Corigliano 934 2002–2011 161 219 2.7 1.5464 0.9830 1.2910 0.9599 0.9518 0.9993 0.9332 0.999017 Cortale 1720 2005–2011 214 470 15.7 1.4452 0.9333 1.0816 0.9775 0.9570 0.9969 0.9163 0.995918 Cosenza 988 1990–2005 287 242 17.3 1.6815 0.9477 1.1053 0.9792 0.9462 0.9924 0.9176 0.991619 Crotone 663 1991–2005 163 5 0.1 1.6870 0.9061 1.2112 0.9827 1.0023 0.9948 0.9515 0.998220 Dinami 1016 2002–2011 224 750 16.6 1.5070 0.9377 1.0978 0.9842 0.9394 0.9904 0.9143 0.990321 Fabrizia 1723 1992–2006 479 948 24.2 1.5149 0.9741 1.0581 0.9879 0.9754 0.9978 0.9437 0.997722 Ferdinandea 1585 1993–2004 372 1050 17 1.4039 0.9840 1.0363 0.9967 0.9906 0.9991 0.9656 0.998623 Feroleto della

Chiesa1045 1991–2005 276 160 13.4 1.5506 0.9474 1.2112 0.9702 0.9772 0.9976 0.9493 0.9974

24 Gambaried’Aspromonte

1598 1991–2000 242 1300 10.3 1.5563 0.9911 1.3317 0.9827 1.0088 0.9992 0.9718 0.9990

25 Giffone 1464 2002–2006 146 594 20.4 1.4791 0.9254 1.2123 0.9684 0.9849 0.9980 0.9547 0.997826 Gioiosa Jonica 908 1999–2006 116 125 5 1.8168 0.9487 1.1299 0.9958 0.9626 0.9984 0.9449 0.998327 Isola Capo Rizzuto 712 1991–2006 189 90 1.7 1.4529 0.9544 1.1098 0.9813 0.8922 0.9903 0.8682 0.993028 Laino Borgo 1411 1992–2011 547 271 18.7 1.5640 0.9399 1.1067 0.9774 0.9594 0.9935 0.9079 0.991129 Lamezia Palazzo 829 1991–2005 233 25 1.2 1.8357 0.9736 1.0722 0.9807 0.9819 0.9984 0.8991 0.996330 Mammola Limina 1986 1992–2006 437 800 14.8 1.5873 0.9615 1.1637 0.9743 0.9742 0.9980 0.9490 0.998231 Monasterace 695 1991–2006 185 70 2.6 1.6564 0.9884 1.0360 0.9941 0.9833 0.9991 0.9617 0.998432 Montalto Uffugo 1364 1990–2006 394 468 8.6 1.6235 0.9540 1.0741 0.9837 0.9670 0.9977 0.9346 0.995933 Montebello Jonico 820.4 2002–2011 142 470 6.9 1.8928 0.9386 1.0773 0.9856 0.9586 0.9962 0.9314 0.996834 Nicastro Bella 1086 1992–2006 378 200 9.9 1.6052 0.9303 1.0922 0.9781 0.9625 0.9952 0.9199 0.995635 Nocelle 1219 1991–2004 324 1315 41.4 1.4422 0.9576 1.0613 0.9863 0.9737 0.9985 0.9380 0.998436 Palermiti 1342 1991–2006 346 480 8.3 1.6794 0.9393 1.2179 0.9768 0.9926 0.9973 0.9430 0.997837 Paola 1071 1992–2003 229 160 1.2 1.8077 0.9485 1.0919 0.9759 0.9547 0.9958 0.9156 0.996138 Papasidero 1569 2005–2011 230 219 10.6 1.5978 0.9317 1.1455 0.9653 0.9577 0.9870 0.9082 0.990239 Petilia Policastro 1068 2003–2007 83 434 31.6 1.4648 0.9565 1.0678 0.9890 0.9703 0.9991 0.9161 0.998640 Petronà 1390 2002–2006 94 889 15.6 1.2973 0.9845 1.1670 0.9953 0.9917 0.9980 0.9707 0.997941 Platì 1776 1992–2006 378 310 15.1 1.5258 0.9275 1.0880 0.9889 0.9599 0.9989 0.9382 0.998942 Reggio Calabria 592 1991–2005 168 15 0.5 1.5962 0.9829 1.2208 0.9836 1.0634 0.9943 0.9607 0.999243 Riace 974 2005–2011 99 304 6.5 1.2204 0.9939 1.3830 0.9869 1.1079 0.9981 0.9688 0.999944 Roccaforte del

Greco1029 1992–2006 216 930 12.5 1.4922 0.9512 1.1088 0.9608 0.9361 0.9973 0.9082 0.9972

45 Roccelletta 598 2002–2006 83 8 1.3 1.5974 0.9827 1.0421 0.9879 0.9631 0.9991 0.9030 0.999446 Rogliano 1202 1991–2007 387 650 22.5 1.6173 0.9502 1.1302 0.9761 0.9362 0.9955 0.8994 0.995747 Rosarno 865 2002–2011 217 61 6 1.5538 0.9732 1.0875 0.9876 0.9501 0.9968 0.9225 0.996948 S. Giovanni in

Fiore1155 1991–2006 206 1050 35.2 1.3045 0.9294 1.1115 0.9851 0.9521 0.9952 0.9055 0.9942

49 S. MarcoArgentano

1287 1990–2007 352 430 15.9 1.6518 0.9457 1.1470 0.9622 0.9743 0.9965 0.9251 0.9981

50 S. MauroMarchesato

799 1997–2006 117 288 15.9 1.5729 0.9700 1.0749 0.9831 0.9038 0.9896 0.8525 0.9894

(Continues)

P. PORTO

Copyright © 2015 John Wiley & Sons, Ltd. Hydrol. Process. (2015)

Table I. (Continued)

Code SitePa

(mm)Studyperiod N

Elev(m a.s.l.)

Dist(km)

60min 30min 10min 5min

a r2 a r2 a r2 a r2

51 S. Nicoladell’alto

976 2002–2011 161 576 12.4 1.5085 0.9713 1.0442 0.9950 0.9769 0.9984 0.9111 0.9983

52 S. Pietro inGuarano

990 1991–2004 277 660 22.7 1.6668 0.9101 1.1196 0.9745 0.9451 0.9954 0.9004 0.9949

53 S. Sosti 1652 1991–2005 371 404 15.9 1.4571 0.9046 1.0904 0.9692 0.9645 0.9951 0.9250 0.995954 Santa Cristina

d’Aspromonte1502 1991–2006 417 510 13.6 1.3661 0.9796 1.1560 0.9823 0.9822 0.9962 0.9510 0.9983

55 Sant’agata delBianco

1050 1992–2004 215 380 6.2 1.3223 0.9621 1.0835 0.9850 0.9707 0.9979 0.9078 0.9976

56 Savelli 1137 2001–2006 61 964 29.1 1.5046 0.9326 1.1636 0.9757 0.9820 0.9897 0.9278 0.994457 Serra S. Bruno 1773 1992–2006 476 790 21.6 1.2692 0.9658 1.0708 0.9886 0.9719 0.9958 0.9252 0.996758 Soverato 879 1991–2011 242 6 0.4 1.6271 0.9308 1.1857 0.9428 0.9552 0.9934 0.9194 0.996659 Staiti 1061 1992–2006 253 550 7.1 1.3172 0.9354 1.0703 0.9890 0.9590 0.9971 0.9141 0.997660 Tarsia 790 1990–2006 240 203 22.8 1.5029 0.9437 1.0474 0.9983 0.8823 0.9919 0.8564 0.995161 Tiriolo 1249 1991–2006 299 690 16.1 1.4121 0.9744 1.0539 0.9936 0.9850 0.9996 0.9474 0.998662 Torano Scalo 861 1991–2005 241 97 10.9 1.5989 0.9450 1.2105 0.9625 0.9452 0.9953 0.9096 0.996763 Tropea 719 1990–2006 242 30 0.2 1.6867 0.9407 1.1546 0.9719 0.9498 0.9947 0.9014 0.994864 Vibo Valentia 949 2000–2006 135 498 3.9 1.2543 0.9885 1.1613 0.9987 1.0133 0.9992 0.9876 0.999265 Villapiana Scalo 493 1990–2011 221 5 0.69 1.7303 0.9469 1.0767 0.9867 0.9650 0.9967 0.9377 0.9966

THE RAINFALL EROSIVITY FACTOR R IN CALABRIA

mountain chains of Aspromonte, Serre, and Sila,characterized by the highest rainfall amount.The rain records used here were collected using

tipping-bucket rain gauges associated with data loggersthat store the records with a temporal resolutionΔt=5min. The observations cover the period from 1990to 2011 with some short breakdown. For some stations, themeasurements at this time resolutionwere not available after2005; consequently, in these cases, the correspondingdataset was reduced in length. However, the number ofstorms,N, and the length of the study period associated withthe name, altitude, distance from the sea, and annual rainfallof each selected rain gauge are listed in Table I.Although in the last few decades the meaning of ‘erosive

event’ has long been debated (Renard et al., 1997; Xie et al.,2002; Dunkerley, 2008, 2010), in this analysis, stormsseparated from other rain periods by more than 6h wereconsidered distinct, and rains of less than 12.8mm wereomitted in EI computation unless as much as 6.4mm of rainfell in 15min (Wischmeier and Smith, 1978). Based on thischoice, each storm was divided intom parts according to thefixed-interval time increments of 5, 10, 15, 30, and 60min.For the temporal resolution of 5, 10, 15, and 30min, the I30term was calculated from the maximum rainfall depthmeasured in a 30-min period, while forΔt=60min, it was setequal to the maximum 60-min accumulated depth. UsingEquations (2), (3a), and (3b), the correspondingEI value wasdetermined for each event and for each temporal resolution.Because of the absence of breakpoint records and

considering that the duration of 15min is reasonably shortenough to obtain constant intensity data (Agnese et al.,

Copyright © 2015 John Wiley & Sons, Ltd.

2006), regression equations of the form of Equation (5)were developed to obtain estimates of (EI30)15 as afunction of (EI30)Δt calculated from the same storm butgenerated from different time increments. Based on thisassumption, for each site, the values of the scaleparameter a of Equation (5) and for the other timeintervals (60, 30, 10, and 5min) were deduced accord-ingly. Calculation of the scale parameter a for the timeintervals of 60 and 30min is of very practical importancebecause, in absence of data recorded at shorter timeintervals, this would be the only way to obtain correctestimates of (EI30)15. The availability of rainfall datarecorded at shorter time intervals (5 and 10min) implies,of course, that it is always possible to use the aggregationcriterion to obtain the real value of EI. However, theanalysis was extended to these shorter intervals in order toemphasize the effect of the time resolution on thecalculation of rainfall intensity as it was already suggestedby other authors (for example, Dunkerley, 2008). Basedon the results obtained in the study area and synthesizedin Table I, even the values of (EI30)5 and (EI30)10 are notequivalent to (EI30)15, and this suggests that care must betaken in calculation of EI.

RESULTS

The temporal variation of the scale parameter a

The values of the scale parameter a obtained fromEquation (5) and for the other time intervals (30, 10, and5min) using the least squares are listed in Table I together

Hydrol. Process. (2015)

P. PORTO

with the values of the determination coefficient r2. Themain statistics of these values, reported for conveniencein Table II, show clearly that as the time incrementdecreases from 60 to 5min, values of EI increase and theestimates of a decrease accordingly.This trend can be observed in Figure 2a where the

mean values of the 65 single estimates of a for each timeinterval are plotted against Δt. The mean values of r2 inTable II show that (EI30)15 and (EI30)Δt are positivelycorrelated, although the coefficient of determination(always greater than 0.9) decreases as the time incrementincreases (Figure 2b).A visual inspection of Figure 2 indicates clearly that

values of EI for time resolutions greater than 15min areunder-predicted, and this confirms the findings of otherauthors in different areas. Thus, when rainfall data at timeresolutions lower than 60min are not available, thederived rainfall erosion index values need a correction toobtain reliable calculations of EI.

The spatial variation of the scale parameter a

Previous studies carried out in Calabria about thespatial variability of R or derived indices (among theothers, Aronica and Ferro, 1997; Ferro et al., 1999;Terranova et al., 2013) showed the existence ofhomogeneous areas within the region. The values of aobtained from Equation (5) and using the different Δtseries are interpolated over the entire region in order toexplore the existence of any spatial trend of thisparameter. The resulting maps, obtained using a linearkriging interpolation procedure, are provided in Figure 3,for each time resolution. A visual inspection suggests thatno geographical dependence can be observed as the fourmaps seem to show different spatial distributions fordifferent Δt. This is also confirmed by superimposing the

Table II. The main statistics of EI30 and the

60 30

μ 1185.7 1562.8σ 614.5 702.8Min 291.6 468.7Max 2834.7 3346.2

μ 1.5325 1.122σ 0.1732 0.073Min 1.1307 1.031Max 1.8928 1.383

Coeμ 0.9536 0.981Min 0.9046 0.942Max 0.9939 0.998

Copyright © 2015 John Wiley & Sons, Ltd.

three pluviometric sub-zones (Tyrrhenian, Central, andIonian) selected in Calabria (Ferro et al., 1999) inFigure 3 (see boundary lines marked in red). It seemsthat the values of a within each sub-zone do not show anyparticular trend or consistence with the overall spatialdistribution, and this suggests the absence of any climaticdependence of the scale parameter a.In order to understand in depth the spatial variation of

a, further attempts are made to explore possiblecorrelations with topography, including elevation (Elev)and distance from the sea (Dist), the latter calculated asthe crow flies from the measuring point to the coastline.In Figures 4 and 5, the values of a, for each station andeach time resolution, are plotted against Elev and Dist,provided as well in Table I.Figure 4 shows clearly that for time resolutions shorter

than or equal to 30min, no correlation exists between thea values and the corresponding elevation. However, evenif no physical explanation can be suggested, a highercorrelation (r2 = 0.214) can be observed for Δt=60min(Figure 4a), suggesting that the effect of altitude becomesmore important as the time resolution increases.A similar tendency can be observed in Figure 5 where

the a values are plotted against the distance from the sea.Although the general correlation is even weaker than thatobserved for the altitude, the value of r2 (0.12) forΔt=60min (Figure 5a) is greater than that for lower timeresolutions. However, considering that the generalcorrelations with both Elev and Dist are very low, theequations superimposed in Figures 4 and 5 are merelyindicative and cannot be used for predicting the values ofa for different time resolutions.A further attempt to find significant correlations with

variables of easier access was carried out considering therelationship between the values of a and those corre-

scale parameter a for each time interval

Δt

10 5

EI301807.8 1884.8817.6 856.3522.9 538.2

3682.5 3900.3Parameter a

5 0.9684 0.92929 0.0321 0.02710 0.8823 0.85250 1.1079 0.9876fficient of determination r2

4 0.9965 0.99688 0.9870 0.98947 0.9998 0.9999

Hydrol. Process. (2015)

0.80

1.00

1.20

1.40

1.60

a

Time interval (min)

a)

0.94

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1

0 20 40 60 0 20 40 60

r2

Time interval (min)

b)

Figure 2. Trend of the values of a observed (a) and the corresponding coefficient of determination r2 (b)

1.31.3

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1.51.5

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JonianSub-zone

JonianSub-zone

TyrrhenianSub-zone

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1.021.041.061.081.11.121.141.161.181.21.221.241.261.281.31.321.341.361.38

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2580000 2620000 2660000 2700000 2580000 2620000 2660000 2700000

2580000 2620000 2660000 2700000 2580000 2620000 2660000 2700000

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a) b)

c) d)

Figure 3. The spatial variation of the a values for Δt = 60min (a), for Δt = 30min (b), for Δt = 10min (c), and for Δt = 5min (d)

THE RAINFALL EROSIVITY FACTOR R IN CALABRIA

Copyright © 2015 John Wiley & Sons, Ltd. Hydrol. Process. (2015)

Figure 4. Relationship between the values of a (for each Δt) and the elevation

P. PORTO

sponding to the mean annual rainfall. These comparisonsare reported in Figures 6 and confirm the same tendencyfor the values of a deduced by higher time resolutions toimprove the correlation.

DISCUSSION

The values of a provided in Table II and depicted inFigure 2a, b show that, according to several authors, thereis a significant dependence of a from the time resolutionΔt used to calculate EI. On the other hand, Figures 3 showthat the spatial distribution of a, as a result of a linearkriging interpolation procedure, is not consistent with theclimatic pattern of the region. These findings suggest, firstof all, that in order to use rainfall data at time resolutiongreater or lower than 15min, the derived rainfall erosionindex values need a correction to obtain reliablecalculations of EI; also, as suggested by Agnese et al.(2006), the relationships expressed in the form ofEquation (5) must be locally calibrated. Based on theseassumptions, the 65 values of (EI30)Δt, related to the meanvalues of EI for each station and for each time resolution,are plotted against the corresponding 65 values of (EI30)15in Figure 7.Each of the four series plotted in Figure 7 can be

approximated by a linear function (r2>0.98) forced tothe origin where the slope represents the value of a forthat series.

Copyright © 2015 John Wiley & Sons, Ltd.

The new values of the scale parameter a generated bythis procedure suggest calculating the value of (EI30)15 byusing the following parametric equation:

EI30ð Þ15 ¼ a Δtð Þ EI30ð ÞΔt (6)

where the parameter a(Δt) can be predicted in turn as afunction of Δt. The new relationship between a and Δt isillustrated in Figure 8.A comparison between Figures 8 and 2a (the latter

based on the mean values of a for the four series) does notshow, at a first sight, a significant difference between thetwo sets of values. However, the approach based on theparametric equation (6) is more robust because the meanvalue of each series is not necessarily a good estimator ofa for that series. In Figures 9 is reported, for each series ofa, the comparison between the corresponding empiricaland theoretical (Gaussian) distributions. Clearly, theempirical distributions of a, with the only exception ofa(60), are generally asymmetric and cannot be represent-ed by the mean value.As a result of a linear interpolation of the pairs plotted

in Figure 8, the following equation is suggested toestimate the value of a for each time resolution Δt:

a ¼ 0:00909Δt þ 0:87158 (7)

where Δt is expressed in minutes.

Hydrol. Process. (2015)

Figure 5. Relationship between the values of a (for each Δt) and the distance from the sea

Figure 6. Relationship between the values of a (for each Δt) and the mean annual rainfall

THE RAINFALL EROSIVITY FACTOR R IN CALABRIA

Although Equation (7) is calibrated on a local scale, thelarge database used for its determination (17139 stormevents) makes it a useful tool to obtain a first estimate of

Copyright © 2015 John Wiley & Sons, Ltd.

EI30 in different areas of the world. If, for example, weconsider the time resolution of 60min, Equation (7) givesa value of a=1.417, which falls satisfactorily in the

Hydrol. Process. (2015)

Figure 7. Relationship between the mean values of EI calculated usingΔt = 15min and the mean values of EI calculated using Δt ranging from 5

to 60min

Figure 8. Relationship between the values of a deduced from Equation (6)and Δt

P. PORTO

overall range provided by the estimates in Sicily (1.297–1.363), Oregon (1.193–1.378), Georgia (1.639), andChina (1.408–1.722).However, precise estimates of the scale parameter a can

be obtained only if a spatial distribution of this parameteris available all over the region of application. The resultsgiven in Figure 3a–d demonstrate that, at least for thestudy area, no geographical dependence can be observedfor this parameter when the time resolution changes.Figures 4, 5, and 6 confirm the difficulty of gettingreliable estimates of a because only weak correlationswith topographic variables and rainfall data are docu-mented. However, for the study area, the results shown inFigure 3 are important because they allow estimates of a

Copyright © 2015 John Wiley & Sons, Ltd.

to be obtained even in areas not covered by rainfallmeasurements for time resolution lower than 60min. Thenumber of stations investigated (65) and used to producethe maps of Figures 3 gives a good opportunity to test thevalidity of the results provided by the linear kriginginterpolation. This test can be performed considering areduced number of stations for providing the map of a fora certain Δt and checking the values of a relating to theremaining stations with the corresponding estimates givenby the map. The analysis was carried out as an examplefor Δt=60. The calibration map illustrated in Figure 10was generated using 45 stations (see white circles inFigure 1), while, for validation, the remaining 20 stations(see black circles in Figure 1) were used.The 45 stations used for calibration were chosen

mainly on the basis of their geographic location in orderto characterize the variability of topography and altitudewithin the study area, while still providing a fairlyuniform spatial coverage (Figure 1).The map plotted in Figure 10, generated by a linear

kriging interpolation procedure with a cell size of 1 km2,shows the same pattern of a as that illustrated in Figure 3awhere the entire dataset (65 stations) was used. The‘residuals’ routine provided by Surfer (Golden Software)was employed to extract the 20 estimates of acorresponding to the 20 stations used for validation.These values were combined with the correspondingvalues of (EI30)60 to obtain the estimates of (EI30)15. Thecomparison is illustrated in Figure 11.The results presented in Figure 11 indicate that the

estimates of (EI30)15, using the values of a obtained fromthe calibration map of Figure 10, are in reasonableagreement with the measured values of (EI30)15, obtaineddirectly from the datasets. This conclusion is furtherconfirmed by the efficiency index of 0.936 obtained forthe relationship between predicted and observed values(Nash and Sutcliffe, 1970). Overall, the good agreementbetween measured and predicted values of (EI30)15suggests that if the relationship between (EI30)15 and(EI30)60 is calibrated on a number of representativestations, a linear kriging interpolation procedure can beused to obtain reliable estimates of (EI30)15 for areas notcovered by rainfall measurements with Δt lower than60min.

CONCLUSIONS

The study reported in this paper has focused on the needto consider the effect of time resolution when the rainfallerosivity factor R of the USLE is calculated from rainfallmeasurements obtained from time intervals greater than15min. The analysis, carried out using 17139 stormevents collected from 65 rainfall stations in Calabria,

Hydrol. Process. (2015)

Figure 9. Comparison between the empirical and theoretical distributions of a for each value of Δt

5

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1.1

1.17

1.24

1.31

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1.45

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1.59

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1.8

1.87

Figure 10. The spatial variation of the a values for Δt = 60min generatedusing 45 stations

Figure 11. Comparison between the measured values of (EI30)15 and thoseobtained from the values of the scale parameter a deduced from the map of

Figure 10

THE RAINFALL EROSIVITY FACTOR R IN CALABRIA

southern Italy, provides general guidance for calculatingR when breakpoint precipitation data are unavailable. Thescale parameter a that represents the conversion factor for

Copyright © 2015 John Wiley & Sons, Ltd.

converting fixed-interval values of (EI30)Δt to values of(EI30)15 is investigated at both temporal and spatial scales.A linear relationship between a and Δt, synthesized byEquation (7), is proposed and can be used as a firstattempt to obtain reliable estimates of the scale parameterin different areas. A parametric equation (Equation (6)),based on the value assumed by a for each time interval, isalso proposed to obtain reliable estimates of EI30 fordifferent time resolutions. Although its efficiency hasbeen tested within the temporal range extending from 5 to60min, a further application for time resolutions greater

Hydrol. Process. (2015)

P. PORTO

than 1 h is in progress in Calabria. This would provide animportant tool to obtain reasonable estimates of R whereonly coarser time resolution data are available. Also, acorrect estimate of EI30 can be crucial in calculating therainfall erosivity factor required as input in other modelssuch as USPED (Stream Power-based Erosion Deposition),SEMMED (Soil Erosion Model for MEDiterraneanregions), and SEDEM (SEdimentDEliveryModel). Finally,the spatial analysis performed on a local scale suggests thatif the relationship between (EI30)15 and (EI30)60 is calibratedon some representative stations, a linear kriging interpola-tion procedure can be used to obtain reliable estimates of(EI30)15 for areas not covered by rainfall measurements withΔt lower than 60min.

ACKNOWLEDGEMENTS

The study reported in this paper was supported by a grantfrom MIUR PRIN 2010–2011. The author is alsoindebted to the ARPACAL for providing rainfall dataused in this study. The paper has benefited from thereviews provided by two anonymous reviewers. Theircomments and suggestions are gratefully acknowledged.

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