Journal of Hydrology 387 (2010) 119–127

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Journal of Hydrology

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MedREM, a rainfall erosivity model for the Mediterranean region

Nazzareno Diodato, Gianni Bellocchi *

Met European Research Observatory, GEWEX-CEOP Network – World Climate Research Programme, Italy

a r t i c l e i n f o

Article history:Received 30 June 2009Received in revised form 8 February 2010Accepted 5 April 2010

This manuscript was handled by L. Charlet,Editor-in-Chief, with the assistance ofS. Yue, Associate Editor

Keywords:Annual time stepErosivity factorMedREM, Mediterranean Rainfall ErosivityModel(R)USLE, Universal Soil Loss Equation and itsRevisions

0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.04.003

* Corresponding author. Tel./fax: +39 0824 61006.E-mail addresses: scodalabdiodato@gmail.com (N

yahoo.com (G. Bellocchi).

s u m m a r y

This paper presents and assesses the model MedREM, in which annual-based climate and rainstorm dataare used to estimate the long-term (R)Universal Soil Loss Equations and its Revisions (USLE) annual rain-fall erosivity over a large region. Two known models of rainfall erosivity (named after the first author ofthe original paper, Torri and Yang) were also assessed and compared with the MedREM. Yang and Torrimodels are both based on the annual precipitation models. MedREM also takes annual maximum dailyprecipitation data into account, and incorporates a longitude-dependent coefficient. The test area wasa large region centered on the Mediterranean basin, in which 66 weather stations were available – 43Italian and 23 out-of-Italy sites (12 countries, about 30–50� latitude North, and 10–50� longitude East) –with multi-year data of (R)USLE annual erosivity. The three models were calibrated against (R)USLE rain-fall erosivity data from 55 stations and evaluated over a validation dataset from 11 Italian stations. On thevalidation dataset, the MedREM estimates generally compared well with the (R)USLE data according toNush–Sutcliffe coefficient (0.87 against 0.76 and 0.73 with Torri and Yang model, respectively). Implica-tions for erosivity modelling were discussed in the context of climatic features concluding that accurateestimations of site-specific annual erosivity for the Mediterranean region require process-based modelwith spatially-explicit parameterization.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

. . . I believe that the world-view implied by modern physics isinconsistent with our present society, which does not reflectthe harmonious interrelatedness we observe in Nature. FritjofCapra, 1990. The Tao of Physics. Adelphi.

Precipitation (mainly rainfall) falling to the Earth’s surface aspart of the water cycle is essential to soil moisture and most terres-trial plant life. However, under particular environmental condi-tions, rainfall is main factor driving soil degradation because itcan erode soils and nutrients by the force of raindrops, surfaceand subsurface runoff (e.g. Zachar, 1982; Lal, 2001). Rainfallaggressiveness has always been a prominent environmental threatin the course of human history, especially affecting the agriculturalsector. However, studies on soil erosion only started in the firstdecades of the 20th century and have increased in number andvariety since then, especially targeting at isolating the role of dif-ferent natural factors on soil erosion (Angulo-Martínez et al.,2009). On recent years, the analysis of rainfall extremes andaggressiveness has attracted the attention of researchers acrossthe world (García-Oliva et al., 1995; Sauerborn et al., 1999; Easter-ling et al., 2000; D’Odorico et al., 2001; Nearing et al., 2004; Schütt

ll rights reserved.

. Diodato), giannibellocchi@

et al., 2007). It has been with the advent of mathematical models ofsoil erosion that rainfall aggressiveness, defined under the name of‘‘rainfall erosivity”, has been systematically analyzed. The Univer-sal Soil Loss Equation (USLE, Wischmeier and Smith, 1978) andits revised forms (RUSLE, Renard et al., 1997; Foster, 2004), makeuse of rainfall erosivity (R-factor) and topographical and land-usefactors for estimating the annual soil loss at different spatial scales.USLE and RUSLE – collectively indicated as (R)USLE – are the mostfrequently adopted approaches worldwide to estimate erosivity ascombined functions of rainstorm intensity and duration, and themass, diameter and velocity of rainfall. However, the applicationof such models to provide annual or long-term erosion hazard esti-mates for a site depends on the availability of sub-hourly precipi-tation (e.g. distribution of rainfall intensities on 10-min). Shorttime-intervals rainfall intensity data are given by either digitizedpluviographs or tipping-bucket technology (discrete rainfall rates)but, in many parts of the world (e.g. the Mediterranean area), re-cords of this type are limited in time and not easily available (Yuet al., 2001). Also for this, the relation between extreme rainfallevents and erosion process has been difficult to assess until nowupon Mediterranean regions (Gonzáles-Hidalgo et al., 2007).

Based on rainfall intensities extracted from the pluviogramcharts, Bagarello and D’Asaro (1994) developed models for calcu-lating erosivity from storm amounts in Sicily Island (Italy), incor-porating 30-min maximum rainfall intensities. Similar attemptswere made by Mannaerts and Gabriels (2000) to estimate the

Table 1Parameter values estimated for models Torri (Eq. (1)), Yang (Eq. (2)), and MedREM(Eq. (3)).

Parameters Erosivity models

Torri Yang MedREM

6850 mm y�1 >850 mm y�1

b0 1.99 0.142 10.4360 0.117b1 �278 1.356 �0.00298 �0.015b2 – – �5889 –a – – – 2.000

120 N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127

erosivity index by using storm amount and duration in Cape Verdeislands (West Africa). However, also in areas where sufficiently anddetailed long time series are available, the number of locations isgenerally insufficient to spatially interpolate erosivity datasetswith confidence (Davison et al., 2005). For such situations, alterna-tive and more simplified procedures are suggested in USLE/RUSLEhandbooks for the estimation of rainfall erosivity index from morereadily available types of precipitation data, such as mean monthlyor annual rainfall. R-factor is not directly linked to annual rainfallamount but cases are given where a good correlation was foundbetween the two variables. For West Africa, for example, the sim-plified relationship linking the average annual R-factor to the aver-age annual rainfall proposed by Roose (1977) was successfullyapplied at some sites but failed for stations at mountainous andcoastal regions, and in tropical transition zones. Working in formerRhodesia, Stocking and Elwell (1976a,b) observed a good relation-ship between mean annual rainfalls and mean R-factor annual val-ues. For Hawaii, Lo et al. (1985) also chose average annual rainfallas the best estimator of average annual R-factor. In continentalUSA, Renard and Freimund (1994) used instead both mean annualprecipitation and the Modified Fournier Index (Arnoldus, 1977) toestimate R-factor. Other authors proposed similar approaches forBelgium (Bollinne et al., 1979), the Bavarian region of Germany(Rogler and Schwertmann, 1981), south-eastern Australia (Yu andRosewell, 1996), Slovakia (Šúri et al., 2002), Taiwan (Lin et al.,2002), the Orissa region of India (Sudhishri and Patnaik, 2004), Iran(Sepaskhah and Sarkhosh, 2005), Bulgaria (Rousseva and Stefano-va, 2006), Benin (Lawal et al., 2007), South Africa (Le Roux et al.,2008), and north-western Spain (Angulo-Martínez et al., 2009).For southern Portugal, a procedure to estimate erosivity index onmonthly scale was presented by de Santos Loureiro and deAzevedo Couthino (2001), based on monthly rainfall amount andfrequency above a fixed threshold. A procedure based on dailyrainfall was instead proposed by Yu et al. (2001) for peninsularMalaysia. With the aim of estimating RUSLE climate inputs, sto-chastic weather generators were also used to produce rain erosiv-ity monthly distribution (Yu, 2002).

In the Mediterranean area, important efforts have been made inthe last decades to reconstruct hydrological regimens from alluvialsequences (Poesen and Hooke, 1997; Bintliff, 2002) and to reporttrends in extreme precipitation indices (Alpert et al., 2002; Lionelloet al., 2006). There is, however, still a lack of long-term records ofrainfall erosivity and storm characteristics for erosion modelling inthis region, where rainstorm impacts are dominated by a widerange of rainy events types and by extreme events too rare to occurin the duration of a research project. In this study, we target at theMediterranean basin with the purpose of estimating annual erosiv-ity values for this wide region, after a long-term monitoring startedin 2000 at Monte Pino Met European Research Observatory, Bene-vento, Southern Italy (Diodato and Bellocchi, 2008a). The erosivityestimation relationships for specific locations remain still difficultto be developed on homogeneous bases of data over broad areaswhere spatial-time variability of climatic variables is high. Therehave been few attempts to assess rainfall erosivity at large spatialscales. At global scale, Yang et al. (2003) identified alternate powerand polynomial relationships between annual values of rainfallerosivity and precipitation. Regional scales were, instead, ap-proached by Diodato (2004) for erosivity estimation in individualyears, and by Torri et al. (2006) for estimating long-term annualerosivity, with both models employed for Italy. We represent herea scale, represented by the Mediterranean basin, intermediate be-tween the global scale and the regional scale in order to guaranteeparsimoniousness of the erosivity model while preserving the dis-tinct properties of a large (sub-continental) region. For the Medi-terranean area, the inter-annual climate variability makes itdifficult to assess patterns in rainfall distribution and impacts of

rainstorms on erosivity (Ramos and Martînez-Casasnovas, 2006).The Mediterranean climate shows indeed a complex pattern ofspatial and seasonal variability, which is exacerbated by the intrin-sic unpredictability of rainfall from year-to-year, within the year,and spatially during a single rainfall event (after Safriel, 2007).For the modelling purpose, apart from changes in the mean cli-matic variables, changes in the variability are of great importanceas well as in the extremes frequency (Katz and Brown, 1992; Schäret al., 2004; Schaeffer et al., 2005).

A parsimonious approach for modelling erosivity factor overlarge areas was adopted in this study by incorporating into modelsfew of relevant variables such as annual precipitation and dailymaximum precipitation, easily available nowadays via web re-sources, and able to capture geographic variability at the scale ofinterest. Based on that, a novel rainfall erosivity model was devel-oped with yearly average time step (referred to hereafter as Med-REM, Mediterranean Rainfall Erosivity Model), linking erosivityfactor to readily available rainfall data to estimate the (R)USLE’sannual erosivity rates over the Mediterranean area. The model, ap-plied over a range of terrains in the Mediterranean region to esti-mate long-term average annual erosivity, was evaluated against(R)USLE-based erosivity data and by comparing it with two alter-native models (Yang et al., 2003; Torri et al., 2006).

2. Materials and methods

2.1. Study area and data sources

The main synoptic conditions responsible for abundant rainsover the Mediterranean region are generally characterized bynorthwesterly or westerly airflow eastward-moving cyclonicdepressions. These depressions are frequently generated over theMediterranean Sea itself (Wigley, 1992) and, reinforced by conti-nental north-easterly airflow, tend to produce important precipita-tion events (Barriendos Vallve and Martin-Vide, 1998). In thesummer period, intense drought events can be associated withhemispheric meridional circulation (i.e. sub-tropical anticyclone)often interrupted by atmospheric instability with shower andthunderstorm. Stormy and aggressive cyclones are characterizedhowever by short life-cycles, with average radius ranging from300 to 500 km (e.g. Lionello et al., 2006), many of which being acombination of both frontal and convective rainstorms. Highly ero-sive rainfalls at Mediterranean sites were found to be characterizedby complex properties (Diodato and Bellocchi, 2009), in which thespatial distribution is organized into clusters of high rainfall local-ized cells embedded within a larger cloud system or clusters oflower intensity (concept of multifractality according to Mazzarella,1999). In all cases, rainfall pattern and storm intensity are bothmain determinants of the observed rainfall erosivity, the latterbeing the ability of rainfall to erode soil (Wischmeier and Smith,1978).

Annual erosivity values calculated with (R)USLE approach fordifferent counties were derived from literature (Table 1). For the

N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127 121

modelling purpose, rainfall data used were derived from tipping-bucket electronic stations, installed by RAN-UCEA (Rete Agromete-orologica Nazionale – Ufficio Centrale di Ecologia Agraria, http://www.politicheagricole.it/UCEA/Stazioni_RAN/Index.htm) at 32Italian sites, and from European Climate Assessment & Dataset(ECA&D) project (http://eca.knmi.nl), for the remaining countriesof the study area (32 stations) which includes Mediterranean andadjacent sites.

The mapping of stations used (Fig. 1) roughly ranges from 30�(Wadi El Ramla, Egypt) to 49� (Huty, Slovakia) latitude north, and8� west (Ouneine, Morocco) to 48� east (Kermanshah, Iran) longi-tude. Elevations above sea level range from 3 m of Trapani (Italy)to 1392 m of Kermanshah (Iran), the average value being about374 m (±375 m standard deviation). Minimum 10 years of rainfalldata were available at each station, covering the period 1994–2006 in Italy and 1980–2000 outside of Italy. For the purposes ofmodel calibration (estimate of model parameters) and validation(model assessment against an independent set of data) the fulldatabase was segregated into two datasets. Since the full databaseis imbalanced towards Italian sites (�2/3 of the database), the cal-ibration dataset (dataset I) was generated to determine modelparameters’ values representing the Mediterranean basin whileincluding data from each country (55 stations) with a subset (32stations) from Italy (Fig. 1, big map). The Italian data not includedin dataset I (11 locations, �1/4 of the full set of Italian stations)were used to create the validation set (dataset II; Fig. 1, smallmap). The Italian sites were split at random into the calibrationand the validation datasets. For its longitudinal extension and cen-tral position in the Mediterranean Sea, and also for both peninsularand insular territories, Italy can be considered representative ofseveral sub-types of Mediterranean climatic features. Indeed Italyfaces cyclogenesis associated with the formation and mainstreamof events of both Atlantic and continental origin. In order to cap-ture all such features at best in the model parameterizations, thechoice was made to keep a large presence of Italian sites in the cal-ibration set.

2.2. Models of rainfall erosivity

At each site, mean yearly rainfall erosivity (MJ mm ha�1 h�1

y�1) values were estimated using three models that are simplifiedapproaches to estimate (R)USLE–climate factor over large regionswhere reliable and long-term information on rainfall intensity isgenerally not available. The model MedREM was developed in this

20°0

20°0

10°0'0"E

10°0'0"E

0°0'0"

0°0'0"

43°0

'0"N

36°0

'0"N

Fig. 1. Location of the stations for use in erosivity mode

study. Other two models estimate erosivity making use of correla-tions between the R-factor and annual rainfall (P, mm y�1).

2.2.1. Torri et al. model (Torri hereafter)Torri et al. (2006) found, for Italy (central Mediterranean), that

rainfall erosivity (RTorri) can be related to the annual rainfall,approximated by:

RTorri ¼ b0 � P þ b1 ð1Þ

with b0 = 3.08 MJ ha�1 h�1, and b1 = �944 MJ mm ha�1 h�1 y�1.

2.2.2. Yang et al. model (Yang hereafter)The Yang estimate of rainfall erosivity (RYang) is (Yang et al.,

2003):

RYang ¼b0 � Pb1 P 6 850 mm y�1

b0 þ b1 � P þ b2 � P2 P > 850 mm y�1

�����

ð2Þ

This model was developed to run at the global scale with the fol-lowing coefficients: b0 = 0.0483 MJ ha�1 h�1, and b1 = 1.610, forP 6 850 mm y�1; b0 = 588 MJ mm ha�1 h�1 y�1, b1 = 1.19 MJ ha�1

h�1, and b2 = 0.004105 MJ mm�1 ha�1 h�1 y�3, for P > 850 mm y�1.

2.2.3. MedREMThis model (RMedREM), based on concepts by Diodato (2004,

2005), is expressed as follows:

RMedREM ¼ b0 � P �ffiffiffi

dp� ðaþ b1 � LÞ ð3Þ

where b0 (MJ ha�1 h�1), b1 (d0.5 mm�0.50�1), and a (d0.5 mm�0.5) arecoefficients, L (�) is site longitude, d is the annual maximum dailyprecipitation (mm d�1) averaged over a multi-year period.

2.3. Model parameterization and evaluation

Calibration and validation datasets were created as in sectionStudy area and data sources.

For each model, the calibration was run pooling the data fromdifferent sites into one set only. Least-square regression analyseswere run to estimate the parameters of both Eqs. (1) and (2). ForEq. (3), parameter values were instead estimated by using theMicrosoft� Office Excel 2003 solver to minimize the square errorof estimation.

The estimated erosivity values by three models were comparedagainst (R)USLE-based values. The agreement between estimatesand (R)USLE values was evaluated by the inspection of 1:1 lines,

40°0'0"E

40°0'0"E

30°0'0"E

30°0'0"E

'0"E

'0"E

43°0

'0"N

36°0

'0"N

l calibration (big map) and validation (small map).

Table 2Calibration and validation datasets: station sites, climate summaries, data availability and sources; P: yearly precipitation; d: annual maximum daily precipitation; R-factor,(R)USLE rainfall erosivity.

Country Station Long. Lat. P d R-factor Years Sources(�) (mm) (mm) (mm) (MJ mm h�1 ha�1 y�1)

CalibrationItaly Agrigento 13.60 37.30 571 70 876 1951–1999 D’Asaro et al. (2007)

Benevento 14.77 41.13 733 47 901 1995–2002 Diodato (2004)Borgo S. Michele 12.90 41.50 801 48 884 1995–2002 Diodato (2004)Caltagirone 14.50 37.20 559 52 724 1951–1999 D’Asaro et al. (2007)Caltanissetta 14.10 37.50 543 58 782 1995–2002 Diodato (2004)Campochiaro 14.52 41.50 1054 78 1772 1995–2002 Diodato (2004)Caprarola 12.17 42.40 964 67 1578 1995–2002 Diodato (2004)Carpeneto 44.70 44.70 835 80 1381 1995–2007 Diodato and Bellocchi (2008a,b)Castel di Sangro 14.10 41.78 1000 78 1578 1995–2007 Diodato and Bellocchi (2008a,b)Chilivani 8.92 40.70 453 35 377 1995–2002 Diodato (2004)Corleone 13.30 37.80 758 45 900 1995–2002 Diodato (2004)Enna 14.20 37.60 905 84 2200 1951–1999 D’Asaro et al. (2007)Fiume Veneto 12.65 46.00 1183 67 2248 1995–2007 Diodato and Bellocchi (2008a,b)Le Croci di Calenzano 11.26 43.94 849 70 1392 1995–2007 Diodato and Bellocchi (2008a,b)Libertinia 14.58 37.50 462 54 829 1995–2002 Diodato (2004)Marsciano 12.37 43.00 640 49 1070 1995–2002 Diodato (2004)Monsampolo 13.80 43.00 721 57 956 1995–2002 Diodato (2004)Montanaso L. 9.47 45.30 841 66 1383 1995–2007 Diodato and Bellocchi (2008a,b)Montevergine 14.72 40.93 1601 89 3213 1995–2007 Diodato and Bellocchi (2008a,b)Palermo 13.37 38.12 565 63 884 1951–1999 D’Asaro et al. (2007)Palo del Colle 16.60 41.00 572 66 780 1995–2002 Diodato (2004)Pontecagnano 14.80 40.70 855 60 1639 1995–2002 Diodato (2004)S. Casciano 11.12 43.70 867 65 1629 1995–2002 Diodato (2004)S. Fista 12.12 43.50 736 47 892 1995–2002 Diodato (2004)S. Pietro 14.52 37.10 530 60 1233 1995–2002 Diodato, 2004Sibari 16.47 39.70 575 56 711 1995–2002 Diodato (2004)Susegana 12.40 45.80 1233 69 2500 1995–2007 Diodato and Bellocchi (2008a,b)Taormina 15.30 37.90 745 100 1717 1995–2002 Diodato (2004)Trapani 12.50 38.00 472 57 607 1951–1999 D’Asaro et al. (2007)Verzuolo 44.60 44.60 975 74 1470 1995–2007 Diodato and Bellocchi (2008a,b)Vittoria 14.50 37.00 53 53 590 1951–1999 D’Asaro et al. (2007)Zanzarina 10.50 45.10 782 53 1250 1995–2007 Diodato and Bellocchi (2008a,b)

Bulgaria Plovdiv 24.65 42.07 520 43 650 1964–1985 Rousseva and Stefanova (2006)Preslav 26.82 43.17 750 45 900 1964–1985 Rousseva and Stefanova (2006)Sofia 23.33 42.70 578 37 1000 1964–1985 Rousseva and Stefanova (2006)Vidin 22.83 44.00 450 37 350 1964–1985 Rousseva and Stefanova (2006)

Croatia Ilok 19.40 45.20 674 47 1100 1973–1997 Kustura et al. (2008)Egypt Wadi El Ramla 34.00 30.00 100 5 68 1997–2000 Khater (2005)

Iran Kermanshah 47.10 34.60 438 44 400 1967–2001 Beedle et al. (2009)*

Tabriz 46.13 38.80 300 24 100 1966–1990 Sepaskhah and Sarkhosh (2005)*

Morocco Ouneine �8.00 31.00 30 30 400 1999–2000 Klik et al. (2002)Portugal Almeidinha �7.73 40.60 800 45 1343 1961–1990 de Santos L. and Azevedo-C. (2001)**

Faro �7.92 37.00 480 55 1211 1961–1990 de Santos L. and Azevedo-C. (2001)**

Tavira �7.65 37.12 57 57 1313 1961–1990 de Santos L. and Azevedo-C. (2001)**

Serbia Snagovo 19.00 44.00 1007 50 1470 1990–2002 Petkovic et al. (1999)

Slovakya Huty 19.60 48.60 850 40 700 1977–1996 Lapin et al. (2009)

Slovenia Sobota 16.10 46.70 804 44 1170 1991–2006 Ceglar et al. (2008)

Spain Biescas 0.40 42.65 1155 60 2000 1971–1992 Renschler et al. (1999)Conde �4.77 37.88 472 40 410 1961–1990 Renschler et al. (1999)Malaga �4.50 36.70 530 70 1350 1961–1990 Renschler et al. (1999)Penedes-Anoia 1.45 42.10 600 69 1100 1971–1992 Renschler et al. (2000)

Tunisia Burgou 9.50 36.00 312 45 680 1970–1994 Hamed et al. (2002)

Turkey Develi 35.83 38.63 366 32 633 1980–1999 _Irvem et al. (2007)Goksun 36.50 38.00 626 50 700 1980–1999 _Irvem et al. (2007)Izmir 27.20 38.50 696 57 1050 1968–1980 Akyurek and Okalp (2006)

ValidationItaly Aliano 16.40 40.40 578 60 848 1995–2007 Diodato and Bellocchi (2008a,b)

Campobasso 14.65 41.57 820 50 920 1995–2007 Diodato and Bellocchi (2008a,b)Loiano 11.32 44.27 801 71 1418 1995–2007 Diodato and Bellocchi (2008a,b)Milano–Brera 9.20 45.47 941 70 1677 1995–2007 Diodato and Bellocchi (2008a,b)Nicosia 14.40 37.80 755 77 1420 1951–1999 D’Asaro et al. (2007)Noto 15.10 36.90 749 80 1921 1951–1999 D’Asaro et al. (2007)Pietranera 13.50 37.50 579 41 776 1995–2007 Diodato and Bellocchi (2008a,b)S. Lucia 40.00 40.00 487 32 490 1995–2007 Diodato and Bellocchi (2008a,b)Sasso Marconi 11.25 44.38 55 55 808 1995–2007 Diodato and Bellocchi (2008a,b)Vernio 11.15 44.03 1395 81 2700 1995–2007 Diodato and Bellocchi (2008a,b)Vigalzano 11.20 46.00 963 64 1295 1995–2007 Diodato and Bellocchi (2008a,b)

* Data supplied by: Iranian Meteorological rganization, http://www.irimo.ir.** Data supplied by: Sistema Nacional de Informacao do Litoral, http://snirh.pt/snirh.php?main_id=4.

122 N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127

N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127 123

while using the modelling efficiency by Nash and Sutcliffe (1970)as performance statistic (with the support of the WHAT model,Purdue University, West Lafayette, IN, USA, https://engineer-ing.purdue.edu/Engr). The latter ranges from negative infinity to1, positive values indicating to which extent the model is a betterestimator than the average value of the measured data ((R)USLEdata in this study). Comparisons were done with the calibrationand the validation datasets, and with a third set given by the cali-bration dataset minus the Italian data.

3. Results and discussion

In this section, (R)USLE-based and modelled erosivity data arepresented and discussed. The three models are evaluated in a com-parative fashion. The assumptions behind the novel modellingsolution (Eq. (3)) are also discussed. Finally, remarks are made con-cerning the bearing of the findings on a wider interpretation ofrainfall erosivity estimation over large regions and the need for fu-ture studies.

3.1. R(USLE)-based rainfall erosivity data

The (R)USLE data were characterized through the use of graph-ical data analysis in a three-tier figure (Fig. 2). This exploratorydata analysis showed evidence of non-normal distribution of an-nual erosivity data. The box-plot (Fig. 2a) reveals an asymmetricaldistribution with two outliers (Saadabad, Iran; Vernio, Italy). Thenormal probability plot of residuals (Fig. 2b) shows deviation froma straight line, whilst the histogram of residuals (Fig. 2c) discloses adistribution skewed right. The spatial distribution of rainfall ero-

0 550 1100 1650 2200 2750 3300

Rainfall erosivity

-150

-100

-50

50

100

150

200

250

-4 -2

a b

Fig. 2. Box-plot (a), normal probability plot of residuals (b), and histogram of the same reoutliers falling outside of the upper limit of the box-plot. X-axis in (b) reports standardi

Nas

b

(R)U

SLE-

base

d da

ta (M

J m

m h

a -1 h

-1 y

-1)

Modelled data (MJ mm ha-1 h-1 y-1) Modelled data (

Nash-Sutcliffe = 0.79

a

Fig. 3. Scatterplots between (R)USLE-based and modelled (Torri model, Eq. (1)) average ain (a) minus Italian stations. The 1:1 and least-squares fit lines are also shown.

sivity indicates annual rainfall erosivity ranges from a minimumof 100 MJ mm ha h�1 y�1 in the Iranian upland (Tabriz) to amaximum of 3213 MJ mm h�1 y�1 at South-Italy mountains(Montevergine), with most of the sites having values of 700–1400 MJ mm h�1 y�1.

3.2. Erosivity models determination and evaluation

The relationships between annual rainfall erosivity and its esti-mators according to Eqs. (1)–(3) were determined. Table 2 showsthe parameter values determined via calibration for the three mod-els. The optimized parameters determined over a pool of data fromall sites help ensure a generic spatial and temporal representation,i.e. a single parameter value was attached at all sites for all years.

For the Torri model (Eq. (1))), the estimated coefficients arequite different from the original values (about �35% and 71% forb0 and b1, respectively). For the Yang model (Eq. (2)), departuresof the estimated coefficients from the primitive values are even lar-ger, especially for the polynomial function where the new esti-mates are radically different from the original proposals.

With the new parameter values, estimated from the data, theTorri and Yang models roughly matched the (R)USLE-based data(Nash–Sutcliffe index >0.70) of both the calibration (Fig. 3a andFig. 4a) and the validation (Fig. 3b and Fig. 4b) datasets. Some dis-crepancies are instead apparent with both models when assessedagainst non-Italian stations of the calibration set. In this case, low-er values of the Nash–Sutcliffe index (�0.50–0.60) are associated toseveral points not lining up around the 1:1 lines (Fig. 3c, andFig. 4c). A better agreement is apparent between (R)USLE-baseddata and MedREM estimates with any dataset (Fig. 5). The

0

0

0

0

0

0

0

0

0

0 2 4Z

Res

idua

l

0

5

10

15

20

25

30

-2s 0 2s

Residual

Freq

uenc

y

c

siduals (c) of (R)USLE-based rainfall erosivity data. Two asterisks in (a) indicate twozed normal values (Z scores).

h-Sutcliffe = 0.76 Nash-Sutcliffe = 0.56

c

MJ mm ha-1 h-1 y-1) Modelled data (MJ mm ha-1 h-1 y-1)

nnual rainfall erosivity data: (a) calibration dataset, (b) validation dataset, and (c) as

(R)U

SLE-

base

d da

ta (M

J m

m h

a -1 h

-1 y

-1)

Modelled data (MJ mm ha-1 h-1 y-1) Modelled data (MJ mm ha-1 h-1 y-1) Modelled data (MJ mm ha-1 h-1 y-1)

Nash-Sutcliffe = 0.76

a

Nash-Sutcliffe = 0.73

b

Nash-Sutcliffe = 0.59

c

Fig. 4. Scatterplots between (R)USLE-based and modelled (Yang model, Eq. (2)) average annual rainfall erosivity data: (a) calibration dataset, (b) validation dataset, and (c) asin (a) minus Italian stations. The 1:1 and least-squares fit lines are also shown.

Modelled data (MJ mm ha-1 h-1 y-1) Modelled data (MJ mm ha-1 h-1 y-1) Modelled data (MJ mm ha-1 h-1 y-1)

Nash-Sutcliffe = 0.88 Nash-Sutcliffe = 0.87 Nash-Sutcliffe = 0.83

a b c

(R)U

SLE-

base

d da

ta (M

J m

m h

a -1 h

-1 y

-1)

Fig. 5. Scatterplots between (R)USLE-based and modelled (MedREM, Eq. (3)) average annual rainfall erosivity data: (a) calibration dataset, (b) validation dataset, and (c) as in(a) minus Italian stations. The 1:1 and least-squares fit lines are also shown.

124 N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127

Nash–Sutcliffe index of 0.80–0.90 reflects indeed little departures ofthe data points from the 1:1 lines. Similar values of the Nash–Sutcliffe index obtained with different datasets indicate, forMedREM, certain stability in the performance across Mediterranean,clue to limited effect the imbalanced presence of Italian sites in thecalibration dataset can have in the estimates. This is not conclusivefor the other two models.

3.3. Modelling assumptions

In Diodato (2004), rainfall data collected at 23 Italian weatherstations during the period 1994–2002 were used to derive a sim-plified relationship for estimating annual erosivity from three mul-tiplicative terms (pluviometrical variables): annual precipitationamount (P), annual maximum daily precipitation (d), and annualmaximum hourly precipitation (h). In the above approach, d andh were introduced as descriptors of the extreme rainfall occurring,respectively, in storms and heavy showers (Diodato, 2005). Thevariable P is, instead, representative of weakly-erosive precipita-tion. The multiplication term (�d � h) was introduced to accountfor storm intensities occurring at different seasons for each rainfallevent. Although long records of meteorological variables do not in-clude hourly rainfall intensities (i.e. the term h), thus limiting thepossibility of applying this approach to elicit historical series oferosivity values, a satisfactory statistical model must continue to

have a relatively small number of parameters suitable to reflectthose aspects in the data that are of scientific interest (after Illianet al., 2008).

To take this into account, h was replaced by the coefficient a(Eq. (4)), in turn modulated by b1 � L (Eq. (3)) according to assump-tion that erosive rainfall tends to decrease from west to east withwesterly storm tracks moving in from the Atlantic into the Medi-terranean Sea. This is reflected in the trend of rainfall erosivityalong the longitudinal profile that decreases towards east(Fig. 6a), and can be also recognized by the role of large scale vari-ables. Fig. 6b shows the vertical profile of the relative humidityestimated for the Mediterranean basin (from NOAA-Physical Sci-ence Division NCEP Reanalysis at http://www.cdc.noaa.gov). Thelongitudinal trend of Fig. 6a tends indeed to agree with the relativehumidity profile that decreases when moving from west to east,especially in near-surface layers (purple-coded sections ofFig. 6b). A positive correlation between rainfall and relative humid-ity in the mid to upper troposphere is known (e.g. Brown andZhang, 1997; Ridout, 2002). Although interplays can be complex,cloud systems generally approach their maximum when sufficientmoisture exists in the middle troposphere (e.g. Geb, 2000).

Enough moisture is needed to sustain thunderstorms, in turnbeing accompanied by heavy, potentially erosive rains. The westto east decreasing trend of rainfall erosivity incorporated in themodel roughly corresponds to Mediterranean cyclogenesis.

Long (°)

800

1000

1500

04030-10 0 10 20 50 4030-10 0 10 20 50

500

0

1600

Rai

nfal

l ero

sivi

ty

2400

3200

4000

Elev

atio

n

a b

57 60 63 66 69 72 75 78 RH(%)

Fig. 6. Mediterranean basin: (a) trend of (R)USLE rainfall erosivity across longitudinal profile, and (b) corresponding profile of the relative humidity (RH) with varyingelevations (from NOAA-Physical Science Division NCEP Reanalysis at http://www.cdc.noaa.gov).

N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127 125

Cyclonic force masses on the Atlantic Ocean off the Iberian westcoast. Cyclones are then pushed westwards while losing strength.However, the Atlantic cyclonic fronts may be reinforced fromseasonal processes occurring in the Mediterranean Sea, mostlyaffecting Italy and adjacent countries (e.g. Lionello et al., 2006).

In previous contributions (van der Knijff et al., 2000; Diodatoand Bellocchi, 2008b), geographic elements were addressed to esti-mate rainfall erosivity in European zones. In this study a similarprinciple was applied up to achieve a satisfactory modelling solu-tion, with longitude dependency.

RMedREM was developed as elaboration of a primitive equation:

RMedREM ¼ b0 � P � ðffiffiffi

dpþXÞ ð4Þ

where X is a linear function (a, intercept, d0.5 mm�0.5; b1, slope,d0.5 mm�0.5 0�1) of longitude (L) that multiplies the annual maxi-mum daily precipitation (d):

X ¼ffiffiffi

dp� ðaþ b1 � LÞ ð5Þ

Eq. (3) results after replacing X with the expression in Eq. (5),where a = 1 + a. Computing it at the study-sites, the term X rangesfrom about 1 (Wadi El Ramla, Egypt) to 9 (Malaga, Spain). Numer-ically, it can be considered a proxy of the frequency of high-inten-sity rain events exhibiting values that approximate the variable dduring the various months of the year. The frequency of high-intensity rain events is indeed critical, as addressed by de SantosLoureiro and de Azevedo Couthino (2001) for Algarve, SouthernPortugal (western-side of Mediterranean Basin), for which thehigher amount of rainfall erosivity comes from the more rainfallthat falls above a certain daily threshold.

Lastly, annual maximum daily precipitation (d) was squarerooted to adjust for site-latitude combinations, inherent to theobservation that precipitation increases with elevation but erosiv-ity generally does not follow the same gradient. This occurs in dif-ferent forms depending on latitude, and would require non-linearsolutions (e.g. Diodato and Bellocchi, 2008b), simplified here toan exponent lower than one (0.5) that complies with the need ofkeeping the model relatively simple.

3.4. Climate implications for erosivity modelling

Based on the evidences of this study, the MedREM (Eq. (3)) isrecommended for annual rainfall erosivity estimations in the Med-iterranean region. The model requires little more work in the pro-cess of parameterization than two-parameter Torri model (Eq. (1))but it is comparable to Yang model (where two or three parame-ters are required depending on the precipitation pattern, Eq. (2)).Unlike their models, its structure incorporates an improved knowl-

edge and the level of accuracy of estimates. This suggests thatparameterization efforts are compensated by the benefit of havinga large amount of information relative to erosivity processes thatcan support the management of natural resources at the scale ofinterest.

In this study, rainfall erosivity modelling relies on generic opti-mised parameters. They are crude estimates over multiple sitesproviding values of general use for application at any location inthe Mediterranean region. If the application of the MedREM toany individual Mediterranean site may be limited by the abilityto provide appropriate, site-representative parameter values ableto capture the variability of erosivity data, this is also true forany other model. Specific geographical locations may have, how-ever, particular characteristics which cause the parameters to devi-ate from reference values, and may require local optimisation.

The maps of Fig. 7 have been selected to represent the strongcharacter of seasonality of rainfall intensities driving the erosivityregimes across different geographical zones of the Mediterranean.They are elaborations from TRMM (Tropical Rainfall MeasurementMission) – based maps, showing three-hourly rain rates over2000–2009 decade. It is evident from these maps that during thecold season (October–April), relatively high rainfall rates are morecommon at lower latitudes (Fig. 7a) and along western facets ofmountainous chains (Italian Apennines and Balcanic Mountains),Turkey southern coasts, western Iberia where perturbations resultin abundant precipitation with release of important quantities ofkinetic energy. On the contrary, the continental regions (north/northeast) are those more likely giving erosive rains (e.g. withinshowers and thunderstorms) in the warm season (May–Septem-ber) (Fig. 7b).

Under particular meteorological conditions these rains may as-sume a chaotic spatial pattern and the erosivity spatial variabilitycan be seen as discrete rather than continuous phenomenon, mak-ing difficult punctual estimation and interpolation. Spatial varia-tion in rainfall depth and rainfall erosivity may have indeedimportant implications for site estimates of these values and formodel simulations that depend on them as input, especially inindividual seasons or years. Dunne and Leopold (1978) reportedthat sparse rain gauge networks in semiarid climate tend to under-estimate rainfall characteristics required for planning, conserva-tion practices, and engineered structures. The potential effects ofsuch spatial variations need to be considered in concert with mod-elling or assessment objectives.

When the relationship between independent and dependentvariables referring to values measured at different locations isnot constant over space, modifying the daily precipitation totalson days with thunderstorms (after Changnon, 2001) and the useof geographically weighted regressions (e.g. Fotheringham et al.,

a b

Fig. 7. Mediterranean three-hourly rain rate maps averaged over (a): October–April, and (b): May–September (2000–2009 decade), arranged by the TRMM-platform usingthe GES-DISC Interactive Online Visualization ANd aNalysis Infrastructure (Giovanni) as part of the NASA’s Goddard Earth Sciences (GES) Data and Information ServicesCenter (http://disc.sci.gsfc.nasa.gov/precipitation).

126 N. Diodato, G. Bellocchi / Journal of Hydrology 387 (2010) 119–127

2002), can be options that generate parameters disaggregated byspatial units. This may allow assessing the spatial heterogeneityin the estimated relationships between rainfall and erosivity overlarge regions and can be considered an evolution of this research.Furthermore, changes in precipitation at seasonal scale must beintegrated into new modelling solutions.

4. Conclusions

There is still an important need for process-based understand-ing and modelling of climatic keys driving soil erosion processesat a range of spatial and temporal scales. The present study offeredan evaluation of a novel model of rainfall erosivity (MedREM),which was used to quantitatively assess the distribution of annualerosivity over the Mediterranean region. The identification of someclimatic keys for rainfall erosivity modelling and scenarios at regio-nal scales (as in this study) is important for understanding therainfall and storms characteristics and their potential impact on lo-cal agricultural and ecological systems. The results obtained in thisstudy encourage also for developing iso-erodent maps and the useof geospatial techniques to model the rainfall erosivity spatial var-iability over Mediterranean area. However, accurate estimations ofsite-specific annual erosivity in the Mediterranean region call forspatially-explicit parameterization. This could be considered anevolution of the present work.

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