Estimating monthly (R)USLE climate input in a Mediterranean region using limited data

Journal of Hydrology (2007) 345, 224–236

ava i lab le at www.sc iencedi rec t . com

journal homepage: www.elsevier .com/ locate / jhydro l

Estimating monthly (R)USLE climate input in aMediterranean region using limited data

Nazzareno Diodato a,*, Gianni Bellocchi b

a Monte Pino Met Research Observatory, TEMS Network-Terrestrial Ecosystem Monitoring Sites (FAO-United Nations),Contrada Monte Pino, 82100 Benevento, Italyb Agrichiana Farming, Abbadia di Montepulciano, Via di Sciarti n. 33/A, 53040 Siena, Italy

Received 25 September 2006; received in revised form 25 July 2007; accepted 15 August 2007

00do

KEYWORDSErosivity factor;Monthly time step;REMDB;Diodato-BellocchiRainfall ErosivityModel;Soil erosion

22-1694/$ - see front mattei:10.1016/j.jhydrol.2007.08

* Corresponding author. Tel.E-mail address: nazdiod@t

r ª 200.008

/fax: +3in.it (N.

Summary This work presents three empirical models (MMFI, Morais Modification of Four-nier Index; GJRM, Grimm–Jones–Rusco–Montanarella; REMDB, Diodato–Bellocchi Rain-fall–Erosivity Model) where monthly-based climate data are used to estimate long-term(R)USLE (Universal Soil Loss Equation and its Revisions) rainfall erosivity factor (Rm,MJ mm h�1 ha�1 month�1). The objective was to evaluate two known models (MMFI andGJRM), and compare the results with the novel model REMDB meant for complex terrains.MMFI and GJRM are both based on the precipitation amount, whilst REMDB takes site lat-itude, elevation and precipitation seasonality also into account. The test area was theItalian region, where 30 stations (altitudes from about sea level up to 1270 m, over thelatitudinal range 36–46�North) with sufficient data to calculate Rm according to USLEwere available. The three models were evaluated against USLE rainfall erosivity over avalidation data set of 14 stations, using a range of performance statistics. The REMDB esti-mates generally compared well with the USLE estimates according to different statistics.For REMDB, the relative root mean square error was, in average, 48.58% against 71.49% forMMFI and 66.55% for GJRM. The average modelling efficiency of REMDB was 0.51 against�0.02 (MMFI) and 0.13 (GJRM). REMDB was also superior in preventing biased errors intime, as quantified by the average pattern index versus months: 17.65 MJ mm h�1 ha�1

month�1, against 58.54 MJ mm h�1 ha�1 month�1 (MMFI) and 57.76 MJ mm h�1 ha�1

month�1 (GJRM). Of the two simplified models, the MMFI was the worst performer whilethe GJRM model performed similarly to the REMDB at two mid-altitude sites of CentralItaly.ª 2007 Elsevier B.V. All rights reserved.

7 Elsevier B.V. All rights reserved.

9 0824 61006.Diodato).

mailto:[email protected]

Estimating monthly (R)USLE climate input in a Mediterranean region using limited data 225

Introduction

Scientists and environmental managers alike are increas-ingly concerned about the effects of hydrological and eco-logical processes on landscape pattern and soil erosion(Renschler and Harbor, 2002; Fu et al., 2005). This has stim-ulated new interest in developing methods for estimation oferosive power of the rainfall (termed erosivity) and, more ingeneral, for soil erosion modelling (Sonneveld and Nearing,2003; Yang et al., 2003a). For Mediterranean regions in par-ticular, most attention is paid on erosional soil degradation(Kosmas et al., 1997; Kirkby et al., 1998; Grimm et al.,2002; Torri et al., 2006). It is also expected that soil re-sources will continue to deteriorate in these areas, probablyas a result of climate change, land use and human activitiesin general (Gobin et al., 2004). Mediterranean area has beendescribed as a transitional bio-climatic ecosystem betweenthe tropics and temperate zones (Lavorel et al., 1998),where a large vegetation biodiversity is adapted to periodicaridity (Osborne and Woodward, 2002). However, due to thelag between rainfall events and vegetation growth, the landsurface is often exposed to intensive rainfall episodes fol-lowed by longer dry periods (Crisci et al., 2002; Van Leeu-wen and Sammons, 2003; Cislaghi et al., 2005; VanRompaey et al., 2005). Such strong seasonal contrast withalternate dry-wet periods is likely to promote water erosionrates in the Mediterranean agricultural areas (Sauerbornet al., 1999; Kosmas et al., 2002).

The Universal Soil Loss Equation (USLE, Wischmeier andSmith, 1978) and its revised forms (RUSLE, Renard et al.,1997; Foster, 2004) are the most frequently applied world-wide for estimating the annual soil loss from rainfall erosiv-ity, topography and land-use. However, application of suchmodels to provide annual or long-term erosion hazard assess-ment for a site depends on knowledge of hourly or sub-hourlydistribution of rainfall intensities. Short time-intervals rain-fall intensity data are given by either digitized pluviographsor tipping-bucket technology (discrete rainfall rates) but,in many parts of the world (including the Mediterraneanarea) records of this type are limited in time (Yu et al.,2001). Also in areas where sufficiently long time series areavailable, the number of locations is generally insufficientto spatially interpolate erosivity data sets with confidence(Davison et al., 2005). In contrast to that, long-term rainfalldata are available for a large number of locations.

When USLE or RUSLE are used for an assessment of the an-nual soil loss at different scales, land degradation hazardmaps are given which incorporate static maps of climate,vegetation classes, relieves and soils, but omit the seasonalpatterns of climate and vegetation growth (e.g., Millwardand Mersey, 1999; Boggs et al., 2001; Shi et al., 2004). How-ever, since erosion from either catchment, regional or globalscale principally depends on the seasonal rainfall regime andvegetation pattern (Kirkby and Cox, 1995; Kirkby et al., 1998;D’Odorico et al., 2001), an estimate of the erosivity to high-er-than-annual time resolution is desirable. The monthly-time step is regarded as suitable for estimating soil erosion(monthly accumulation of eroded soil from consecutive rainevents) and put it in relation to both the length of cropseasons and the agricultural practices (Diodato, 2005).As pointed out by Yu et al. (2001), monthly distribution of

erosivity is also needed to calculate the USLE/RUSLE averageannual cover and management factor, which in turn is re-quired to estimate annual soil erosion rates.

Models which compute soil loss from an area must neces-sarily include a number of factors such as climate, vegeta-tion, soil topography and land management (Amore et al.,2004). However, the extensive application of simplifiedmodels is difficult because of the large uncertainty associ-ated to their output (see, for instance, Van Rompaeyet al., 2005). Several options on how to fill in this gap forestimation of rainfall erosivity index are suggested in theRUSLE handbook (Renard et al., 1997). For erosivity, themost widely cited approaches accounting for the climaticinfluence refer to the Fournier index (Fournier, 1960), itsmodified forms (Arnoldus, 1977; Renard and Freimund,1994; Yang et al., 2003b), and simple rain-power functions(Rosewell and Yu, 1996). Such approaches target at annualestimates and are not suitable for assessing monthly erosiv-ity. In order to incorporate monthly or seasonal climate fac-tors for rainfall-related erosivity estimates (Renschleret al., 1999; Grimm et al., 2003), models of different com-plexity and nature may be required for different regions(see Loureiro and Couthino, 2001; Petrovsek and Mikos,2004; Silva, 2004; Davison et al., 2005; Mikos et al.,2006). The model from Morais et al. (1991) is a modifiedform of the Fournier index (referred to hereafter as MMFI).Grimm et al. (2003) proposed an erosivity model (referredto hereafter as GJRM) which uses monthly average rainfallonly. Other empirical relationships followed for differentareas of the world (Salles et al., 2002). An alternative ap-proach is to incorporate into erosivity models a certain num-ber of relevant variables such as monthly average rainfalland geographical characteristics, not difficult to detectand able to capture climate and geographic variability atboth regional and sub-regional scales.

A novel rainfall erosivity model with monthly averagetime step (referred to hereafter as REMDB), linking monthlyerosivity factor (Rm) to monthly rainfall amount, and includ-ing the effect of climate and site elevation, was developedwith the purpose to skip over limitations observed whenboth the MMFI and the GJRM model are applied in complexterrains. The REMDB incorporates a monthly sinusoidal func-tion that is modulated by elevation and latitude to accountfor seasonal shifts in rainfall intensity. REMDB was applied toa range of terrains in Italy. At the same sites, REMDB esti-mates were compared with both the MMFI and the GJRMestimates.

Materials and methods

Study area

A modelling study was performed at Italian sites. This areais centrally placed in the Mediterranean basin, character-ized by land use diversity and geographical features includ-ing a large latitudinal gradient, with transition zones fromsemi-arid to humid mountain climate (Lionello et al.,2006). The Mediterranean basin represents a source ofwater for the surrounding areas because the moisture re-leased through evaporation from sea water is re-distributed

226 N. Diodato, G. Bellocchi

by the atmospheric circulation in the form of precipitation(Fernandez et al., 2003). In this area, rainfall intensity isthe most important factor driving water-related soil ero-sion. Water erosion hazard is expected to be high in springand autumn, when soils are likely subject to tillage and ex-posed to high rainfall intensities (Fig. 1). In the cold season,rainfall is principally caused by fronts associated with theMediterranean cyclone, while stormy events with the high-est hourly or half-hourly intensity occur over May–October(Diodato, 2005). In this period, extreme rainfall events lar-gely contribute to erosion hazard in Mediterranean Europe.Especially in dry Mediterranean lands, precipitation is inher-ently variable in amount and intensity and, as a conse-quence, the same variability affects rainfall and runofferosivity (WMO, 2005). It is evident from Fig. 2 that Italyis one of the most vulnerable Mediterranean countries interms of exposure to erosional soil degradation. In this re-gion, the timing of rainfall plays a crucial role in soil erosionleading to land degradation. An erratic start to the rainyseason along with heavy rain likely has a great impact on soilerosion since the seasonal vegetation will not be availableto intercept the rainfall or stabilize the soil with its rootstructure (WMO, 2005).

Precipitation data source

Historical precipitation data from high-resolution measure-ments from 30 Italian sites (5–30 years, Table 1) were de-rived from tipping-bucket electronic stations, installed byUCEA-RAN (Ufficio Centrale di Ecologia Agraria – Rete Agro-meteorologica Nazionale, http://www.politicheagricole.it/UCEA/Stazioni_RAN/Index.htm) since 1994. The mapping ofstations used, roughly ranging from 36� to 46� latitude North(Fig. 3), represents different geographical zones and the

Figure 1 Map of 1961–1990 mean daily rainfall intensity in Aprildata source: IWMI (http://www.iwmi.cgiar.org) Atlas’s 10 min arc

station distribution is consistent with the spatial variabilityof Italian climates. As shown in Fig. 3, the full database wassplit into two data sets (I, II). The data set I (16 stations) wasused to determine model parameters (calibration datasets). The data set II (14 locations) was used for evaluatingmodel estimates (validation data set). The calibration dataset was selected in such a way to both represent the entirestudy area and including a wide range of elevations (i.e.from 3 to 810 m a.s.l.) and distances from the coast (i.e.from 1 to 115 km). The validation data set also includedsites representative of the Italian lands, with elevations be-tween 12 and 1270 m a.s.l., and distances from the coastbetween 1 and 125 km.

For precipitation intensity, the official rain-gauges cur-rently in use in Italy are the tipping-bucket electronicrain-gauge stations of the network UCEA-RAN (Espositoand Beltrano, 1996). The UCEA-RAN gauge is 36 cm high,has an orifice area of 0.04 m2 and mounted with the orifice0.4 m above the ground surface. The gauge has a collectingfunnel and outer container made of high strength plasticwhich minimizes adhesion of rain water on the gauge sur-face, and a clear plastic inner container, graduated for di-rect reading to the nearest 0.2 mm.

The rainfall factor, R, of both USLE and RUSLE is anumerical descriptor of the ability of rainfall to erode soil(Toy et al., 2002). In the paper of Wischmeier and Smith(1978), the rainfall factor was calculated by an empiricalrelationship of the measured 30 min-rainfall intensities.For a given location, the monthly values of R (Rm) are givenby the sum of all the single-storm EI30 values for the monthof interest. The term EI30 (MJ mm h�1 ha�1) is the productof storm kinetic energy (E), calculated over time steps ofminutes of constant storm intensity, and the maximum30 min-intensity (I30) (Renard et al., 1997). The EI calcula-

(a), and October (b) for the Mediterranean area. Precipitationresolution (about 20 km).

http://www.politicheagricole.it/UCEA/Stazioni_RAN/Index.htm

http://www.politicheagricole.it/UCEA/Stazioni_RAN/Index.htm

http://www.iwmi.cgiar.org

Figure 2 INRA-model based (through the web site http://eusoils.jrc.it) annual soil erosion hazard in Mediterranean areas,estimated using empirical rules to combine data on land use, soil crusting susceptibility, soil erodibility, relief and meteorologicaldata (modified after Grimm et al., 2002).

Table 1 Calibration and validation data sets: code number (see Fig. 3), sites, climate summaries, data availability and source

Code number Site Elevation(m)

Latitude(�)

Longitude(�)

Distancefrom thecoast (km)

Precipitation(mm)

Years Sourcea

Calibration1 Susegana 67 45.85 12.40 48 1220 1994–2003 RAN2 Zanzarina 40 45.11 10.50 130 778 1994–2003 RAN3 Verzuolo 420 44.71 07.29 81 893 1995–2002 RAN4 Monteombraro 727 44.43 11.00 64 1045 1956–1985 Calzolari et al.

(2001)5 Cesena 44 44.10 12.25 14 865 1966–1979 Biagi et al.

(1995)6 San Piero a Grado 3 43.72 10.38 90 819 1994–2003 RAN7 Marsciano 229 43.00 12.35 6 638 1994–2003 RAN8 Monsampolo 43 42.90 13.78 9 727 1994–2003 RAN9 Castel di Sangro 810 41.65 14.10 62 932 1998–2004 RAN

10 Benevento PianoCappelle

230 41.11 41.12 46 722 1994–2003 RAN

11 Palo del Colle 191 41.02 16.70 12 594 1994–2003 RAN12 Santa Lucia 14 39.99 08.67 5 473 1994–2002 RAN13 Sibari 10 39.76 16.47 4 586 1997–2004 RAN14 Palermo 50 38.10 13.42 1 574 1998–2004 OAP15 Pietranera 158 35.53 13.50 27 588 1994–2003 RAN16 San Pietro 313 37.12 14.52 25 831 1997–2004 RAN

Validation17 Vigalzano 539 46.05 11.27 135 963 1999–2004 RAN18 Montanaso

Lombardo83 45.37 09.48 110 840 1994–2003 RAN

19 Carpeneto 230 44.71 08.53 103 880 1994–2003 RAN20 Sasso Marconi 128 44.44 11.27 83 839 1982–1990 Calzolari et al.

(2001)21 Vicarello di

Volterra152 43.70 10.48 46 711 1964–1990 Bazzoffi and

Pellegrini (1991)22 Santa Fista 311 43.51 12.13 60 776 1994–2003 RAN23 San Casciano 230 43.70 11.14 64 867 1994–2003 RAN24 Caprarola 650 42.40 12.10 42 969 1994–2003 RAN25 Campochiaro 502 41.50 14.50 65 1099 1994–2003 RAN26 Borgho S. Michele 12 41.48 12.86 2 878 1998–2004 RAN27 Montevergine 1270 40.90 14.74 31 1680 1997–2004 RIRC28 Pontecagnano 29 40.67 14.80 4 818 1995–2003 RAN29 Aliano 250 40.33 16.37 41 638 1999–2003 RAN30 Libertinia 183 37.52 14.65 46 463 1994–2003 RANa RAN, Rete Agrometeorologica Nazionale (Esposito and Beltrano, 1996); OAP, Osservatorio Astronomico di Palermo (unpublished);

RIRC, Rete Idrometeorologica della Regione Campania (unpublished).


http://eusoils.jrc.it

Figure 3 Location of the stations (code number as in Table 3)for use in calibration (black circles) and model validation (greycircles).


tion involves the analysis of hyetographs for each rainevent, excluding rains with less than 13 mm depth and atleast 6 h distant from the previous or the next events, butincluding showers of at least 6.35 mm in 15 min (Wischmeierand Smith, 1978). In this study, rainfall values were notavailable on intervals of minutes, and the USLE climate fac-tor was computed using the indirect approach derived byBagarello and D’Asaro (1994) original relationship for theMediterranean areas, as follows:

EI30 ¼ j � d � ðhmaxÞ1:195 ð1Þ

where d is the daily rain depth (mm d�1), hmax is the maxi-mum 60 min-rain intensity (mm h�1), and j is a coefficientequal to 0.150 (originally set equal to 0.117 when 30 min-rain intensity was computed). This approach was adoptedto replicate erosivity actual values because both the indi-rect, based on an empirical relationship for calculating E,and the direct USLE approach, based on measured kineticenergies, suggest that the effect of the rainfall measure-ment interval (for intervals of 5–60 min) on the rainfall en-ergy characteristics is negligible (Agnese et al., 2006). Toexclude snow days from analysis, Eq. (1) was not computedfor precipitation days when minimum air temperature waslower than or equal to 1 �C.

Long-term average monthly rainfall erosivity factor (Rm,MJ mm h�1 ha�1 month�1) was computed as

Rm ¼1

n

Xny¼1

Xsa¼1ðEI30Þa ð2Þ

where a indicates the number of storms in a monthly period,n is the number of years considered. USLE-based Rm esti-mates were taken as ‘‘true’’ values of monthly rainfallerosivity.

Models of rainfall erosivity

For each site, mean monthly erosivity factor (Rm, MJ mmh�1 ha�1 month�1) values were estimated using threemodelsbased on a combination of monthly inputs.

Morais’s et al. modification of Fournier Index(MMFI)

The MMFI (Morais et al., 1991) estimate of Rm is

Rm ¼ b0pm

P

� �b1ð3Þ

where pm (mm month�1) is monthly average precipitationamount, P (mm year�1) is yearly precipitation, b0(MJ mm h�1 ha�1 year�1) and b1 are empirical coefficients(originally estimated equal to 36.849 and 1.0852,respectively).

Grimm et al. model (GJRM)

Grimm et al. (2003) adopted a simple algorithm on a per-sonal communication (Zanchi C.A., University of Florence,Italy), suggesting that erosivity in Tuscany (central Italy) isproportional to the cumulative yearly rainfall amount. Theauthors have further extended the original model on amonthly scale over the Italian peninsula. Monthly averageprecipitation (pm, mm month�1) is the only input requiredto estimate Rm, as follows:

Rm ¼ b0 � pm ð4Þ

The empirical coefficient b0 (MJ h�1 ha�1 month�1) wasoriginally suggested to vary between 1.1 and 1.5 and succes-sively set to 1.3 by Grimm et al. (2003).

Rainfall erosivity model for complex terrains(REMDB)

The following non-linear equation was developed to esti-mate monthly erosivity factor (Rm):

Rm ¼ b0 � ½pm � ðfðmÞ þ fðE; LÞÞ�b1 ð5Þ

where pm (mm month�1) is monthly average precipitationamount, b0 (MJ mm h�1 ha�1 month�1) and b1 are empiricalparameters, f(m) is a sinusoidal monthly function, f(E, L) isa parabolic function reflecting the influence of site eleva-tion (E, m) and latitude (L, �) on the erosivity.

The f(m) varies with month (m: 1 (January), . . ., 12(December)), after Yu et al. (2001) and Davison et al.(2005), as follows:

fðmÞ ¼ a � 1� b cos 2pm

cþm

� �� ð6Þ

where a, b, and c are empirical coefficients.The equation f(E, L) is as follows:

fðE; LÞ ¼ d þ e �ffiffiffiEpðLc � LÞ þ g

ffiffiffiEpðLc � LÞ

h i2ð7Þ

where E (m) is elevation, L (�) is latitude, Lc (�) is a criticallatitude, and d, e (m�0.5 deg�1) and g (m�1 deg�2) areempirical coefficients.

Model parameterization and evaluation

The empirical parameters of each erosivity model weredetermined using the data set I (calibration). The numberof years with rainfall data available at each site was not

Table 3 Parameter values estimated for MMFI (MoraisModification of Fournier Index), GJRM (Grimm–Jones–Rusco–Montanarella) and REMDB (Diodato–Bellocchi RainfallErosivity Model)

Parameters Erosivity models

MMFI GJRM REMDB

b0 22.3 1.68 0.207b1 0.687 – 1.561a – – 0.3696b – – 1.0888c – – 2.9048d – – 0.3024e – – 1.3848E � 03f – – �1.38092E � 05Lc (�) – – 41


enough for a site-specific calibration, so the calibration wasrun pooling the data from different sites into one set only.Basically, parameter values were estimated against meanmonthly Rm-USLE estimates by using the Microsoft� OfficeExcel 2003 solver to minimize the square error of estima-tion. An iterative calibration process was employed for Eq.(5). First, the set of parameters was determined for f(m)(Eq. (6)) and f(E, L) (Eq. (7)) fitting the Rm values keepingconstant the parameters of Eq. (5). Next, the parametersof Eq. (5) were calibrated against the Rm-USLE estimates.The process was reiterated up to reach a convergingsolution.

Computed Rm values were compared against Rm-USLEvalues. The agreement between estimates and Rm-USLE val-ues was evaluated by the inspection of 1:1 lines and, limitedto the validation data set, through elementary statistics(mean, standard error) and by a set of performance statis-tics organized in modules (accuracy, correlation, pattern)according to the scheme of Bellocchi et al. (2002). The per-formance statistics used were (Table 2): relative root meansquare error (RRMSE), modelling efficiency (EF), probabilityof null mean difference by the paired Student t-test (P(t)),Pearson’s correlation coefficient of the estimates versusmeasurements (R) and two pattern indices (2-group,range-based, Donatelli et al., 2004), one computed versusmonth of year (PImonth), and the other versus monthly pre-cipitation ðPITmin

Þ. Dedicated libraries provided with the toolIRENE_DLL (Fila et al., 2003) were used for computing theperformance statistics.

For a selected number of locations included in the valida-tion data set, the differences between mean monthly esti-mates and USLE data were calculated and plotted against

Table 2 Multiple-statistics assessment: modules and basic statis

Module Statistic

Accuracy (magnitude ofresiduals)

Relative root mean square error

Modelling efficiency

Probability of paired Student t-tfor mean difference being null

Correlation (betweenestimates andmeasurements)

Pearson’s correlation coefficientthe estimates versus measureme

Pattern (presence/absence ofpatterns in residuals)

Pattern index by month of year

Pattern index by precipitation

the month of year, to illustrate the temporal distributionof mean monthly errors over the period of a year and indi-cate possible systematic model behaviour.

Results

Table 3 shows the parameter values determined via calibra-tion for the three models. For the MMFI, estimated coeffi-cients b0 = 22.3 and b1 = 0.687 are quite different (about�39% and �37%, respectively) from the MMFI values(b0 = 36.849, b1 = 1.0852) originally reported by Moraiset al. (1991). For the GJRM model, the estimate of b1

tics

Abbreviation Value, range and purpose

RRMSE 0 to positive infinity: the smallerRRMSE, the better the modelperformance. A dimensionless indexallowing comparisons among a rangeof different model responsesregardless of units

EF 1 to negative infinity: bestperformance given when EF = 1,negative values of EF indicating thataverage value of the measured valuesis a better estimator than the model

est P(t) 0–1: best value is P(t) = 1, and theworst is 0.

ofnts

R �1 (full negative correlation) to 1(full positive correlation): the closervalues are to 1, the better the model

PImonth 0 to positive infinity: the closervalues are to 0 the better the model.Month of year (from 1 to 12) is anindependent variable

PIp 0 to positive infinity: the closervalues are to 0 the better the model.Monthly precipitation is anindependent variable


(1.561) is �30% higher than the original value (b1 = 1.3).These parameter values, estimated from the data, roughlymatched the Rm-USLE data of both the calibration (Fig. 4)and the validation (Fig. 5) data sets. With the two simplifiedmodels (MMFI, GJRM), both figures show a poor agreementbetween estimated and USLE-based values, as several pointstend not to line up around the 1:1 line. A better agreementis apparent with REMDB.

Results from the elementary statistics (mean and stan-dard error) are given in Table 4. The performance statisticresults are detailed in Table 5.

Overall model performance

In general, the REMDB gave the best results (Table 5),according to all but P(t) performance statistics. However,at certain sites, each model showed abilities to providethe best estimates for different individual performance sta-tistics whilst also providing the worst for others. For in-stance, the GJRM model had the best and the worstpattern index against precipitation (PIp): 4.26 at Pontecag-nano, and 162.53 at Montevergine. The same GJRM modelhad the best Student t-test probability (P(t) � 1) at Carpe-neto, but it also had the worst square error (RRMSE =117.63%) at Sasso Marconi. The MMFI had the poorest Stu-dent t-test probability (P(t) = 0.01) at San Casciano, Capra-rola and Montevergine. REMDB was in general the best modelto prevent errors from showing patterns against time (inaverage, PImonth = 17.65 MJ mm h�1 ha�1 month�1 against

Figure 4 Scatterplots between estimated and measured rainfall eof Fournier Index; GJRM: Grimm-Jones-Rusco-Montanarella; REMDB

data set.

Figure 5 Scatterplots between estimated and measured rainfall eof Fournier Index; GJRM: Grimm–Jones–Rusco–Montanarella; REMD

data set.

58.54 and 57.76) and precipitation (in average, PIp = 36.80MJ mm h�1 ha�1 month�1 against 43.23 and 45.38) but, atsome sites, one or both the other models performed betterin terms of PIp. The MMFI had the best PIp at San Casciano(38.12 MJ mm h�1 ha�1 month�1), Santa Fista (33.52 MJmm h�1 ha�1 month�1), Campochiaro (46.38 MJ mm h�1 ha�1

month�1), Montevergine (109.44 MJ mm h�1 ha�1 month�1),and Libertinia (23.64 MJ mm h�1 ha�1 month�1). The GJRMmodel had the best PIp at Vigalzano (54.89 MJmm h�1 ha�1 month�1) and Pontecagnano (4.26 MJ mmh�1 ha�1 month�1) and, at Vigalzano, it also had the bestPImonth (14.37 MJ mm h�1 ha�1 month�1).

Performance of Morais’s et al. modification ofFournier Index (MMFI)

In general, the MMFI highly under-estimated the USLE-basedvalues (mean value 80.0 MJ mm h�1 ha�1 month�1 against120.4, Table 4). The MMFI estimates had also a much lowerstandard error than USLE data (mean standard error equalto 13.1 MJ mm h�1 ha�1 month�1 against 25.7, Table 4), sonot being able to reproduce the observed variability.

Combining all performance metrics computed, the MMFIwas the poorest performer (Table 5). Mean relative rootmean square error (RRMSE) of the MMFI was the highest(71.49%). Such a bad performance was observed at all sites,with the exception of Sasso Marconi and Santa Fista whereRRMSE was a little lower with this model (93.38% and73.32%) than GJRM (117.63% and 85.04%). Student t-test

rosivity values with the three models (MMFI: Morais Modification: Diodato-Bellocchi Rainfall Erosivity Model), on the calibration

rosivity values with the three models (MMFI: Morais Modification

B: Diodato–Bellocchi Rainfall Erosivity Model), on the validation

Table 4 Mean values and standard errors of monthly erosivity factor for USLE (Universal Soil Loss Equation), MMFI (MoraisModification of Fournier Index), GJRM (Grimm–Jones–Rusco–Montanarella) and REMDB (Diodato–Bellocchi Rainfall ErosivityModel) at each site

Evaluation site Mean Standard error

USLE MMFI GJRM REMDB USLE MMFI GJRM REMDB

Vigalzano 107.9 88.3 134.8 76.2 30.1 18.6 21.6 19.6Montanaso Lombardo 132.0 76.7 117.7 100.6 38.1 9.4 10.7 20.2Carpeneto 123.3 81.5 123.3 94.3 28.1 16.9 17.8 23.2Sasso Marconi 69.1 75.8 117.5 80.9 17.8 7.1 8.0 13.6San Casciano 135.5 78.6 121.4 92.3 18.6 10.6 11.9 17.1Santa Fista 76.7 73.2 108.6 81.9 17.6 10.3 11.5 17.2Vicarello di Volterra 92.4 67.8 99.5 74.7 18.0 6.9 7.4 13.1Caprarola 139.1 86.5 135.7 105.4 23.3 14.8 17.4 20.6Campochiaro 152.0 93.6 153.9 142.3 33.7 14.7 18.0 25.4Borgo San Michele 115.8 82.8 123.0 107.4 24.2 16.7 19.3 24.7Montevergine 285.6 128.2 235.3 279.2 53.7 24.2 34.5 52.0Pontecagnano 120.3 77.3 114.5 94.0 22.3 12.8 15.0 19.6Aliano 70.2 56.3 80.8 59.2 17.6 9.4 9.9 12.0Libertinia 66.1 53.7 64.8 41.7 16.9 11.6 10.9 10.3

Mean 120.4 80.0 123.6 102.1 25.7 13.1 15.3 20.6


error probability of rejecting the null hypothesis of equalmean difference was in general low but acceptable (0.24in average). The mean difference resulted significantlydeparting from zero (P(t) 6 0.05) at five sites (San Casciano,Caprarola, Borgo San Michele, Montevergine, Pontecag-nano). Modelling efficiency (EF) was also poor, the averageEF being a negative value (�0.02). Negative EF values wereobserved at six sites (Sasso Marconi, San Casciano, Vicarellodi Volterra, Campochiaro, Montevergine, and Pontecag-nano) while EF approached zero at Montanaso Lombardo.In all other sites, EF values were also low and never largerthan 0.5 unless at Vigalzano (EF = 0.52). According to thecorrelation coefficient (R), the MMFI and the GJRM modelhad the same response in average (R = 0.47). High correla-tion (R P 0.70) between the MMFI and USLE estimates wasobserved at four sites only (Vigalzano, Carpeneto, Capraro-la, Borgo San Michele), whilst a negative correlation wasregistered at Sasso Marconi (R = �0.03).

The MMFI was also the poorest model in preventingestimates from showing patterns in the error with time(average PImonth = 58.54 MJ mm h�1 ha�1 month�1). Monte-vergine manifested a poor pattern index versus month(PImonth = 187.06 MJ mm h�1 ha�1 month�1). PImonth wasquite good and comparable to the ones computed with theGJRM model and the REMDB at Vigalzano (22.07 MJ mmh�1 ha�1 month�1) and Santa Fista (16.34 MJ mm h�1

ha�1 month�1). The average performance of the MMFIaccording to PIp was only slightly better than the one ofthe GJRM model (43.23 and 45.38 MJ mm h�1 ha�1 month�1,respectively).

Performance of Grimm et al. model (GJRM)

The GJRM model estimates were, in average, substantiallyequivalent to the USLE data (mean value 123.6 MJmm h�1 ha�1 month�1 against120.4,Table4), and ithad lowerstandard error (15.3 MJ mm h�1 ha�1 month�1 against 25.7).

In general, the GJRM model had an intermediate perfor-mance to the MMFI and the REMDB, according to the set ofperformance metrics computed (Table 5). The GJRM modelwas better than the MMFI for RRMSE (66.55% in average) andEF (0.13 in average), but R statistic was the same (0.47 inaverage for both models). RRMSE was quite high at all sites(the maximum, 117.63%, registered at Sasso Marconi) but itresulted the best at San Casciano (RRMSE = 50.70%) andCaprarola (RRMSE = 36.43%). EF was negative at five sites(Sasso Marconi, San Casciano, Vicarello di Volterra, Campo-chiaro, and Montevergine) and higher than 0.5 at two sitesonly: EF = 0.55 at Vigalzano, EF = 0.57 at Caprarola (best va-lue at this site). The GJRM model was the best modelaccording to Student t-probability (average P(t) = 0.58),and gave the best absolute P(t) value at Carpeneto (�1).In only one case (Sasso Marconi), the Student t-test resultedsignificant in a probability of 0.03. The GJRM model wassimilar to the MMFI as regards the correlation coefficientvalues at each site. As for the MMFI, R was negative at SassoMarconi (�0.02). The GJRM model was slightly better thanMMFI for PImonth but slightly worse for PIp. The two modelswere similar to each site for both pattern indices. The GJRMmodel gave the worst PImonth at Montevergine(188.90 MJ mm h�1 ha�1 month�1) and the best PIp at Pon-tecagnano (4.26 MJ mm h�1 ha�1 month�1).

Diodato–Bellocchi Rainfall Erosivity Model(REMDB)

In average, the REMDB was observed to only slightly under-estimate the USLE values (mean value 102.1 MJ mmh�1 ha�1 month�1 against 120.4, Table 4) but with quitesimilar variability (mean standard error equal to 20.6against 25.7). The REMDB showed considerably better meanperformance statistics with the exception of the Student t-probability. For this statistic, the performance of the REMDB

Table

5Perform

ance

statisticva

luesusedto

assess

MMFI

(MoraisModifica

tionofFo

urnierIndex),GJR

M(G

rimm–Jo

nes–

Rusco–Montanarella)andREMDB(Diodato–Bellocc

hiRainfallErosivity

Model)ateach

site

Eva

luationsite

Accuracy

Correlation

Pattern

RRMSE

(%)

P(t)

EF

RPI m

onth

(MJmm

h�1ha�1month�1)

PI p

(MJmm

h�1ha�1month�1)

MMFI

GJR

MREMDB

MMFI

GJR

MREMDB

MMFI

GJR

MREMDB

MMFI

GJR

MREMDB

MMFI

GJR

MREMDB

MMFI

GJR

MREMDB

Vigalzano

64.01

62.42

49.21

0.35

0.18

0.03

0.52

0.55

0.72

0.76

0.79

0.95

22.07

14.37

14.95

70.99

54.89

62.19

MontanasoLo

mbardo

95.58

85.45

62.45

0.13

0.68

0.20

0.00

0.20

0.57

0.52

0.52

0.86

33.38

28.73

10.43

42.21

34.93

23.44

Carpeneto

64.26

54.11

37.66

0.06

�1.00

0.02

0.28

0.49

0.75

0.70

0.70

0.93

58.75

60.23

21.76

22.01

17.68

16.23

SassoMarco

ni

93.38

117.63

67.66

0.73

0.03

0.40

�0.19

�0.89

0.38

�0.03

�0.02

0.65

43.15

42.01

4.90

66.32

71.06

61.19

SanCascian

o63

.38

50.70

50.84

0.01

0.50

0.02

�0.93

�0.24

�0.24

0.21

0.17

0.59

53.42

54.53

20.74

38.12

44.91

51.60

Santa

Fista

73.32

85.04

47.52

0.84

0.09

0.64

0.08

�0.24

0.61

0.36

0.37

0.81

16.34

16.39

9.93

33.52

39.94

47.46

VicarellodiVolterra

65.93

61.19

40.06

0.17

0.68

0.10

�0.04

0.10

0.61

0.35

0.34

0.85

62.30

62.31

25.79

34.61

32.32

11.95

Cap

rarola

52.75

36.43

36.97

0.01

0.83

0.02

0.10

0.57

0.56

0.76

0.76

0.86

39.56

39.49

4.80

38.04

24.20

17.55

Cam

poch

iaro

77.65

67.77

43.06

0.09

0.95

0.63

�0.11

0.15

0.66

0.40

0.41

0.82

85.65

83.43

11.46

46.38

63.32

51.57

BorgoSanMichele

51.25

43.43

25.29

0.05

0.64

0.34

0.45

0.61

0.87

0.80

0.79

0.94

73.81

72.49

16.57

34.79

19.08

4.77

Monteve

rgine

80.38

62.78

46.64

0.01

0.35

0.88

�0.66

�0.01

0.44

0.36

0.37

0.71

187.06

188.90

56.31

109.44

162.53

116.29

Ponteca

gnan

o65

.19

55.61

50.03

0.05

0.78

0.14

�0.12

0.18

0.34

0.48

0.48

0.70

50.93

51.21

5.69

8.89

4.26

4.71

Alian

o82

.31

81.17

61.99

0.43

0.54

0.40

0.02

0.05

0.44

0.34

0.35

0.69

44.16

41.43

10.93

36.24

37.93

10.02

Libertinia

71.44

67.94

60.81

0.39

0.93

0.03

0.29

0.36

0.49

0.59

0.60

0.86

49.04

53.05

32.90

23.64

28.25

36.20

Mean

71.49

66.55

48.58

0.24

0.58

0.27

�0.02

0.13

0.51

0.47

0.47

0.80

58.54

57.76

17.65

43.23

45.38

36.80

Italicizednumbers

show

thebest

result

perstatistic.


was similar to that of the MMFI, with significant t-test at fivesites (Vigalzano, Carpeneto, San Casciano, Caprarola, andLibertinia). RRMSE was much better with the REMDB

�48.58% in average, and ranging between 25.29 (BorgoSan Michele) and 67.66 (Sasso Marconi) – than with theother models. Modelling efficiency was also much higherwith the REMDB (0.51 in average) than with the other mod-els. San Casciano proved to be a difficult site to estimatefor the REMDB as well, this model giving the same negativeEF value observed with the GJRM model (EF = �0.24). Afairly strong correlation between REMDB and USLE estimateswas observed (0.80 in average) at almost all sites (R = 0.59,observed at San Casciano, was the minimum). The perfor-mance of the REMDB in terms of pattern indices was alsoquite good (in average, PImonth = 17.65MJ mm h�1 ha�1 month�1 and PIp = 36.80 MJ mm h�1 ha�1

month�1). The superior performance of the REMDB wasclearly evident with PITmonth at each site whilst, at somesites, the other models performed better in terms of PIp.

Deviation of estimates from Rm-USLE values

Fig. 6 illustrates the temporal distribution characteristics,for each model, of deviations from monthly USLE erosivitydata for selected sites. Although to a lesser extent withthe REMDB, all models tend to deviate from USLE values,with over- or under-estimations at particular months or sea-sons. Relevant under-estimations in summer time are appar-ent at San Casciano (placed in central Italy andcharacterized by poor modelling efficiency, Table 5), whileSasso Marconi (located in Northern Italy and characterizedby high square errors, Table 5) shows some over-estimationsin winter months. A peculiar site is Montevergine, where abig deviation between models and USLE estimates is givenin the month of September.

Discussion

The new erosivity model

The model proposed (REMDB) includes two semi-parametricfunctions, both modulating the erosivity intra-seasonal re-gime. The first function, f(m), is a time-related genericmodulator for all sites reproducing a cyclical pattern, whilstf(E, L) adjusts the estimate for each site and latitude com-bination. The rationale behind the development of f(E, L) isinherent to the observation that Rm factor generally de-creases with elevation, but non-linearly and in a differentform depending on the latitudinal gradient. For the latter,latitude equal to 41� was approximated as a threshold inEq. (7): Rm decreases considerably more above than belowthis threshold. The non-linear interaction between latitudeand altitude effects, translated into f(E, L), is depicted inFig. 7. This non-linear correlation is related to the kineticenergy of rainfall, which is influenced by the median rain-drop size and the terminal velocity of free-falling raindrops.

The idea of threshold latitudes for identifying areas whereerosivity is modelled with alternative models is not new. Intheir annual estimates on the European scale, Van der Knijffet al. (2000) isolated two latitudinal thresholds: above48�North, a ‘‘Bavarian’’ equation was assumed to be

Figure 6 Deviation of estimates from USLE monthly erosivity factor versus month of year for MMFI (Morais Modification of FournierIndex), GJRM (Grimm–Jones–Rusco–Montanarella) and REMDB (Diodato–Bellocchi Rainfall Erosivity Model) at selected sites.

Figure 7 Qualitative relationship between elevation, latitudeand function f(E, L). Black arrows correspond to the directionsof the respective axes. Internal arrows are indicative of thechanges of function f(E, L) for different elevation–latitudecombinations.


representative for northern European conditions; below42�North, a ‘‘Tuscan’’ equation was otherwise assumed suit-able for southern-European conditions; a fuzzy-based solu-tion was adopted for the transition between north andsouth. A crisp threshold was regarded as appropriate forour study to discriminate between north and south Italy. Inparticular, the 41st parallel passes not far below Rome(placed at latitude 41.87�North) and roughly marks the bor-der of the prevalently Mediterranean climate characterizingsouth Italy. Frontal autumn–winter rains are typical formountainous sites of southern Italy and tend to be moreintensive as elevation increases, with major release of

precipitable water (orographic precipitations) contrastingthe absence of drop accretion. High-altitude air tempera-tures are relatively high, usually turning into rainy precipita-tions at any period of the year. Conversely, above thelatitude threshold and especially at high sites, small dropsare more typical then large drops because of the absenceof pronounced accretion (Caton, 1966). Snowfalls are alsomore frequent at higher latitudes and, naturally, snow doesnot generate erosivity. Relationships of this type betweenerosivity and elevation–latitude combinations are consis-tent with the results from similar researches in Southern Italy(Ferro et al., 1991) and Central America (Mikhailova et al.,1997).

Model performance

The optimised parameters determined over a pool of datafrom all sites help ensuring a generic spatial representation,i.e. a single parameter value was used at all sites. The threemodels evaluated were able to produce monthly-based ero-sivity factor data to represent both the amounts and pat-terns of USLE values. The REMDB gave the best results interms of multiple performance statistics. The two simplestmodels generally produced worse statistics than the REMDB

but, when examining the individual performance statisticsat specific sites, some diverse responses were observed.The REMDB was roughly the best with respect to all perfor-mance statistics, although there were some poor perfor-mances considering the response across some locations fordiverse statistics. However, for sites where the REMDB re-sponded worse than the other models, only little differ-ences were apparent among model performances. At SanCasciano, for instance, a better accuracy of the GJRM modelfigures out, mainly due to the probability of null mean dif-ference by the paired Student t-test (P(t) = 0.50 against0.02 with the REMDB), whereas other statistics suggest thetwo models are quite similar. Likewise at Caprarola, theaccuracy measures of the GJRM model are better, whilstthe REMDB performed better in terms of pattern indices


and correlation. At both these sites, the two models can beappraised as equally good. This is not the case for siteswhere the REMDB performed better than the two simplifiedmodels. Where estimates are quite poor with the MMFIand GJRM models (e.g. Sasso Marconi, Montevergine, Vica-rello di Volterra), this paper has shown that correction fac-tors of the REMDB are able to account for influential factorspotentially distorting the Rm estimates. The performancemeasures were also computed for the calibration data set.They are not shown in the paper, but the following fewexamples are discussed. For the REMDB, EF was equal to0.79 at San Piero a Grado (coastal site of Central Italy),against 0.36 and 0.51 with the MMFI and GJRM models,respectively. At Palermo (coastal site of Sicily), the differ-ence between the REMDB (EF = 0.74) and the other modelswas even larger: MMFI, EF = 0.19; GJRM, EF = 0.28. At Casteldi Sangro (high hill close to the critical latitude of 41�), EFwas 0.55 for the REMDB, negative (�0.30) for the MMFI mod-el and approaching zero (0.16) for the GJRM model. Theother results gained from the calibration set are not dis-cussed, but these few examples confirm the superiority ofthe REMDB in providing more accurate Rm estimates thanits competitors.

Localised climates and site-specific characteristics couldbe attributed to some results for each model. The negativemodelling efficiency values registered at San Casciano withall models may be due to an unusually high value of erosivity(1675 MJ mm h�1 ha�1 month�1 against 213 as average forthe month), observed in July 1994 and which may have dis-torted the relationship between erosivity and rainfall whenaveraged over 10-year records. Similar considerations canbe attributed to Sasso Marconi (which shows high values ofRRMSE with all models), where only nine years of data wereavailable and few data unusually low were observed inspring and autumn months. A big discrepancy was observedin September at Montevergine (Fig. 6), which may be par-tially explained by the high variability of extreme precipita-tion events occurring at this site in late summer. This site ofSouth Italy is the highest (1270 m a.s.l.) of those evaluated,and falls outside the range of elevations explored throughthe calibration process. Snowfalls may be also frequent atMontevergine in winter, so the real erosive precipitation(rainfalls) happens with irregularity in this season and withinter-annual variability. The high variability observed inthe 9-year records available at this site, potentially distort-ing the estimates of parameters to the extent that they donot belong to the main population, stands behind the choiceof leaving Montevergine out of the calibration set and par-tially explains the discrepant results.

This investigation has used generic optimised parame-ters, which are crude estimates over multiple years, butdo provide values of general use for any application in thesame sites. The REMDB may appear more sensitive to varia-tion in its several parameters than the MMFI and the GJRMmodel are to their few parameters. The application of theREMDB to other Mediterranean sites may therefore be lim-ited by the ability to provide appropriate site-representa-tive parameters able to capture the temporal variabilityof erosivity data. Specific geographical locations may haveparticular characteristics which cause the parameters todeviate from reference values, and may require local opti-misation. A spatial sensitivity analysis goes beyond the goal

of this study, but testing the stability of model parametersat changing conditions might be required in view of general-ized applications of the REMDB. However, some consider-ations may be set forth which indicate that theparameters of Eqs. (6) and (7) can display a potential stabil-ity across sites. The cosine function of Eq. (6) used here ap-proaches the same seasonal fluctuation of rainfall erosivitywhich is common to vast areas of the world, including Med-iterranean sites (Yu et al., 2001; Yu, 2002; Petrovsek andMikos, 2004; Davison et al., 2005). As regards the factorsof elevation–latitude interaction (parameters d, e and gin Eq. (7)), such parameters were estimated from optimiza-tion against Rm-USLE estimates from elevations and lati-tudes in a wide range (Table 1), so they can be consideredas being quite stable for the ranges explored. Parametersb0 and b1 of Eq. (5) might actually require local calibrationto rescale the relationship against elevation–latitude inter-actions, but this calibration is equally required for the MMFIand, limited to parameter b0, for the GJRM model. For thesemodels, parameter values in Table 3, much different thanthose originally set up by the model developers confirmthe need of local calibration.

Conclusions

When only rainfall data are available on a monthly basis, itis preferable to use the REMDB to estimate long-termmonthly mean erosivity factor, rather than simplified mod-els not accounting for the interaction with elevation andlatitude. The results have demonstrated that the MMFI isunsuitable to give reliable estimates of monthly erosivity,while the GJRM model is capable of making better estimatesat some locations. The REMDB did not show sizeable system-atic, seasonal estimation errors, whereas the MMFI andGJRM models more frequently displayed seasonal under-or over-estimations. The seasonal variability which gener-ally appears greatest in the highest altitudes emphasizesthe need of using extended weather records for modellingpurposes at these sites. Outlying data are more commonat high elevations and can lead to a false perception of mod-el goodness when limited data sets are used for validation.Long calibration series are also recommended for high-alti-tude sites to minimize distortion in parameter estimates. Ingeneral, since variations in weather patterns from year-to-year can affect the long-term mean erosivity, long seriesare required for accurate estimates. This study is probablyaffected by some climatic trends not completely identifiedin the short meteorological records in many of the stationsavailable in the country. Short data sets not representativeof long-term erosivity may put some limitations on modelestimates. However, the comparative evaluation of models,although underpowered for conclusive findings about calcu-lated erosivity values for some stations, seems sufficientlycomplete to support the basic features of the REMDB for reli-able estimates.

The limited number of meteorological stations availablein Italy and elsewhere with suitable Rm-USLE data raises theneed for considerable refinement of the proposed model,and hence improvement in model estimates. Considerationsabout model adequacy should be given to the model perfor-mance as illustrated by the use of a range of assessment


statistics, supported by some form of graphical representa-tion of the temporal pattern of error distribution. Hence,researchers and practitioners wanting to create completemonthly climate data sets, i.e. observed precipitation sup-plemented with modelled erosivity factor, need to be awareof the behaviour of the models and how introduced errorsmay manifest themselves in the purposes to which the dataare put. Similar consideration needs to be given to localisedweather phenomena, with practitioners being aware of howthis may impact on model estimates.

Besides some superiority of the REMDB, the results gainedwith this study have shown the value of using a combinationof assessment statistics to provide a comprehensive illustra-tion of model performance. Such an approach is recom-mended in order to provide valuable information on themagnitude and pattern of errors that may occur when esti-mated data are combined with USLE data to fill in the gapand create complete data sets. Aggregation of multiple sta-tistics into synthetic indicators of model validity is possibleusing fuzzy-based rules (Bellocchi et al., 2002; Rivingtonet al., 2005; Diodato and Bellocchi, 2007a,b), provided thatinformation is available about acceptance/rejection crite-ria and relative weight of each performance measure. Suchknowledge is still lacking in the context of erosivity modelevaluation. For this reason, the various statistics used formodel validation were left disaggregated and no summaryvalidity measures were reported in the present study.

Acknowledgements

Dr. Mrs. Nilantha Gamage (International Water ManagementInstitute, Battaramulla, Sri Lanka), Dr. Fabrizio Ungaro (Re-search Institute for Hydrogeologic Protection of the ItalianResearch National Council, Florence, Italy), Dr. Vincenzo Iuli-ano (Palermo Astronomical Observatory, Italy) and FatherAmato Gubitosa (Meteorological Observatory of Montever-gine Sanctuary, Italy) are gratefully acknowledged for facili-tating the collection of the weather data used in this work.

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Documents

Estimating monthly (R)USLE climate input in a Mediterranean region using limited data