A NEW METHODOLOGY FOR ESTIMATING RAINFALL
AGGRESSIVENESS RISK BASED ON DAILY RAINFALL RECORDS FOR
MULTI-DECENNIAL PERIODS
Leoncio Ga cía-Ba ón1, Julia Mo ales2, A u o Sousa2*
1 Depa amen o de Física Aplicada II, Uni e sidad de Se illa, E-41012 Se illa, España
2 Depa amen o de Biología Vege al y Ecología, Uni e sidad de Se illa, E-41012
Se illa, España
ABSTRACT
The empo al i egula i y o ain all, cha ac e is ic o a Medi e anean clima e,
co esponds o he i egula i y o he en i onmen al e ec s on soil. We used
agg essi eness as an indica o o quan i y he po en ial en i onmen al impac o ain all.
Howe e , quan i ying ain all agg essi eness is condi ioned by he lack o sub-hou ly
equency eco ds on which in ensi y models a e based. On he o he hand, olume
models a e cha ac e ized by a lack o p ecision in he ea men o hea y ain all e en s
because hey a e based on mon hly se ies. The e o e, in his s udy, we p opose a new
me hodology o es ima ing ain all agg essi eness isk. A new syn hesis pa ame e
based on e o mula ion using daily da a o he Modi ied Fou nie and Oli e ´s
P ecipi a ion Concen a ion indices is de ined. The weigh ing o bo h indices o
calcula ing he agg essi eness isk is es ablished by mul iple eg ession wi h espec o
he local e osion R ac o es ima ed in he las decades. We concluded ha he p oposed
me hodology o e comes he p e iously men ioned limi a ions o he adi ional in ensi y
*Co espondence o: A. Sousa, Depa amen o de Biología Vege al y Ecología, Uni e sidad de Se illa, E-41012 Se illa, Spain. E-
mail: [email protected]
*Re ised manusc ip wi h no changes ma ked
Click he e o iew linked Re e ences
and olume models and p o ides accu a e in o ma ion; he e o e, i is app op ia e o
de e mining po en ial ain all impac o e long ime pe iods. Speci ically, we applied
his me hodology o he daily ain all ime se ies om he San Fe nando Obse a o y
(1870-2010) in sou hwes Eu ope. An in e annual agg essi eness isk se ies was
gene a ed, which allowed analysis o i s e olu ion and de e mina ion o he empo al
a iabili y. The esul s imply ha en i onmen al managemen can use da a om long-
e m his o ical se ies as a e e ence o decision making.
KEY WORDS: Agg essi eness; Rain all e osi i y; Land use; En i onmen al isk;
Sou hwes Eu ope
1. In oduc ion
One o he ea u es o he ain all egime in a Medi e anean clima e is he in e - and
in a-annual i egula i y (Ga cía-Ba ón e al., 2013). In e -decadal clima e s udies help
o explain he causes o e ain al e a ion o e ime (Dioda o e al., 2008). Rain all
e osi i y causes a loss o e ile soil, damage o ag icul u e and in as uc u e and wa e
pollu ion and is in luenced by changes in ain all pa e ns (Ma ín-Fe nández &
Ma ínez-Nuñez, 2011; Sánchez-Mo eno e al., 2014) and by p edic able e ec s o
clima e change (Dioda o e al., 2011). In his s udy, we conside agg essi eness isk as a
po en ial es ima e o he physical e ec s o ain all on soil dynamics sensu Fou nie
(1960). Ou iew is ha agg essi eness isk is an app op ia e en i onmen al indica o
and di ec ly ela ed o e osion and associa ed wi h he incidence o o en s, loods,
landslides, displacemen , e c. (G ego i e al., 2006). The e o e, knowledge o his
a iable o e long pe iods is pa icula ly use ul o he managemen o wa e esou ces,
soil conse a ion, ag icul u al planning and he de elopmen o en i onmen al policy.
Mo eo e , annual es ima es o agg essi eness isk enable he compa ison o o de s o
magni ude among di e en obse a ion si es a di e en imes. This en i onmen al
indica o is based on daily ain all eco ds and does no include o he aspec s ela ed o
e osion such as slope leng h, soil ypes, wind ac i i y, land use, e c.
Fo he di ec calcula ion o soil e osion, he uni e sal soil loss equa ion (USLE)
has been equen ly used (Wischmeie & Smi h, 1978). Speci ically, he ain all
e osi i y, o R ac o , depends on he ene gy o e e y ain all episode (Panagos e al.,
2015). The R ac o is an accep ed ins umen o local e osion measu emen ,
successi ely upda ed and empi ically endo sed by means o ield measu emen s (Rena d
e al., 1997). Models such as he USLE and RUSLE we e o iginally de eloped o
de ailed scale applica ion in he a ming sec o , so hei applica ion on a egional scale
p esen s some limi a ions (Te ano a e al., 2009). Al hough USLE is one o he mos
widely used e osi i y models wo ldwide, i has some limi a ions because he
es ima ions o soil e osion do no i he empi ical measu es o sedimen a ion, and he R
e osi i y ac o does no explici ly inco po a e di ec uno o wa e , which a ec s he
accu acy o he model (Kinnell, 2010). Addi ionally, he spa ial dis ibu ion ends o
o e es ima e he R ac o a egional o i e basin le els (He nando & Romana, 2016),
and i s is no ecommended in a eas di e en om hose in which i was de eloped
wi hou an analysis o he alidi y o he equa ions.
In he speci ic case o he s udy o ain all agg essi eness e ec s, wo
complemen a y app oaches a e aken: in ensi y models a e based on sub-hou ly ain all
eco ds, and olume models a e based on mon hly ain all eco ds. This model e e s o
he di e en pa ial accumula ions o ain all. Tha is, i does no ake in o accoun he
numbe , he du a ion and he ain all amoun
exclusi ely on he o al mon hly ain all. Ne e heless o he di ec calcula ion o he
ain all e osi i y in la ge a eas, i is desi able o make use o high equency ain all
eco ds collec ed by nea by wea he s a ions du ing a pe iod longe han wen y yea s
(Angulo-Ma inez e al., 2009). Howe e , excep o mode n au oma ic wea he
s a ions, adi ional obse a o ies ha e no high- equency se ies wi h sub-hou ly
eco ds. On he o he hand, olume models a e based on mon hly ain all eco ds ha
a e ex ensi ely a ailable in mos coun ies. In his case, he egula use o he
agg essi eness index in en i onmen al s udies (Fou nie , 1960), subsequen ly modi ied
by A noldus (1980) as he Modi ied Fou nie Index (IFM) and complemen ed wi h he
P ecipi a ion Concen a ion Index (IPC) de eloped by Oli e (1980), is ema kable.
Bo h es ima ions o calcula ing he in ensi y o ain all agg essi eness p esen
limi a ions. The d awback o he in ensi y models is he lack o adequa e ime se ies
eco ds, and ha o he olume models is he imp ecision in he ea men o hea y ain
episodes because hey a e based on ine imescale esolu ions. The amoun o
p ecipi a ion is no he only ele an pa ame e ; i s empo al dis ibu ion is also ele an ,
as s udies on Medi e anean i e basins in he NE Ibe ian Peninsula (Sánchez-Canales
e al., 2015) and in he SW Ibe ian Peninsula (Sousa e al., 2009) ha e made e iden .
Va ious s udies ha e compa ed he esul s ob ained using in ensi y models ( he R ac o
o USLE) o hose ob ained using olume models. In he Ibe ian Peninsula, he Ins i u e
o he Conse a ion o Na u e (ICONA, 1988) unde he Spanish Minis y o
Ag icul u e p oposed an empi ical ela ionship ha locally associa es he R ac o wi h
he IFM index. Addi ionally, a high co ela ion be ween he R ac o and he mon hly
and/o annual p ecipi a ion pa ame e s, including he Fou nie Index, has been ob ained
in a ious geog aphic a eas, such as in he Medi e anean a ea (Dioda o & Bellocchi,
2007; Taguas e al., 2013), Eas Asia (Lee &Heo, 2011; Yue e al., 2014) and he
opical zone (Sanchez-Mo eno e al., 2014). In he USA, Rena d & F eid (1994)
p oposed eg ession equa ions ha calcula e he R ac o om IFM. Addi ionally,
Lou ei o & Cou hino (2001) es ima ed he R ac o based on he mon hly ain all
agg essi eness in sou he n Po ugal, and Da Sil a (2004) es ima ed he same in B azil.
In his s udy, we p opose o es ima e he agg essi eness isk by means o a
single annual pa ame e ha imp o es he limi a ions o models based only on mon hly
eco ds ( olume models) and hose based on sub-hou ly eco ds (in ensi y models). We
used a me hod based on he daily scaled e o mula ion o he adi ional indices o
agg essi eness, IFM and IPC, ha p o ides mo e accu a e esul s. The me hod also allows

nume ous in es iga ions because he e a e many wea he s a ions ha ha e la ge ime
se ies o daily da a. This Es ima ed Annual Agg essi eness Risk (RA) is calib a ed
locally by means o eg ession equa ions wi h espec o he e osi i y R ac o o a
pe iod o simul anei y. Backwa ds ex apola ion o he esul ing unc ion gene a es he
co esponding ime se ies o he agg essi eness isk. Recen ly, Ga cía-Ba ón e al.
(2015) ha e syn hesized in his pa ame e he agg essi eness isk using IFM and IPC o
s udy ends in i e basins o he Ibe ian Peninsula. In his a icle, we p opose wo main
objec i es:
a) To de ine and calcula e a single annual pa ame e based on daily eco ds
ha syn he ically es ima es he ain all agg essi eness isk.
b) To apply his me hodology o a s udy a ea wi h a Medi e anean clima e
o analyse he empo al beha iou and deduce pa e ns in he e olu ion o
he ain all agg essi eness isk.
2. S udy a ea and da a
We chose he Sou h-A lan ic egion o he Ibe ian Peninsula o he me hodological
applica ion, which is based on a long pe iod and can help o d aw conclusions abou he
po en ial isks o ain all on he land. Spain is one o he coun ies mos se e ely
a ec ed by soil e osion in he Eu opean Medi e anean egion due o ex eme spa ial
and empo al a ia ions in i s physical en i onmen , wi h equen pe iods o d ough
and o en ial ain all (Solé, 2006). The impo ance o e osion in he Medi e anean is
ela ed o he long his o y o human ac i i y in a egion cha ac e ized by low annual
p ecipi a ion, he occu ence o in ense ains o ms and long-las ing d ough s, high
e apo anspi a ion, he p esence o s eep slopes and he occu ence o ecen ec onic
ac i i y, oge he wi h he ecu en use o i e, o e g azing and a ming (Ga cía-Ruiz e
al., 2013).
The sou hwes e n Ibe ian Peninsula alls wi hin he domain o he Medi e anean
clima e, al hough i is in luenced by an oceanic e ec because o i s p oximi y o he
A lan ic Ocean. The a e age annual ain all is app oxima ely 600 mm (a e age alues
a e subs an ially highe in he moun ain ange sepa a ing he wa e sheds o he
Guadiana and Guadalqui i i e s). Rain all is subjec o ma ked in e -annual
i egula i y, wi h g ea oscilla ions in annual o als ha include mul i-yea pe iods o
d ough (Aguila , 2007). In gene al, he p o ile o he in a-annual p ecipi a ion shows
an asymme ic unimodal cu e, ascending in au umn and descending smoo hly om
win e o summe , when i eaches i s minimum.
The Royal Obse a o y o he Spanish Na y (ROA) loca ed in San Fe nando
(p o ince o Cadiz, a he sou he n ip o he Ibe ian Peninsula) includes he oldes
ac i e wea he s a ion in Spain; ain all eco ds ha e been eco ded since 1805 and
accessible daily da a since 1870. Because o hese long- e m and high-quali y eco ds,
di e en s udies ha e used ROA da a as a e e ence o cha ac e ize he ain all egime
(Rod igo, 2002; Ma in-Vide & Lopez-Bus ins, 2006) and he in e - and in a-annual
beha iou (Ga cía-Ba ón e al., 2013) o ain all in he s udy a ea.
The me eo ological s a ions loca ed in he p o ince o dis ic capi als o Spain
and Po ugal ha e been selec ed o quan i y he le el o egional ep esen a ion o he
ROA ain all se ies (Figu e 1). Da a om he Spanish s a ions we e p o ided by he
Spanish Me eo ological Agency (AEMET), and da a om he Po uguese s a ions we e
p o ided by he Po uguese Sea and A mosphe e Ins i u e (IPMA). The wea he s a ions
a e dis ibu ed o e di e en geog aphical a eas as ollows: Cadiz, Huel a and Fa o in
he coas al zone, Co do a and Se ille in he Guadalqui i alley, and Badajoz and Beja
in he Guadiana basin (Figu e 1).
Figu e 1. Map showing he loca ions o he me eo ological s a ions used in he s udy
a ea.
These se ies a e homogeneous and ha e no missing da a (Alma za e al., 1996;
Ga cía-Ba ón e al., 2013). We ha e chosen he pe iod 1961-1990, ecommended by
he Wo ld Me eo ological O ganiza ion, o compa ing he ROA ain all eco ds o
hose o e e y selec ed egional s a ion. Table 1 shows he ep esen a i eness o he
ROA compa ed o e e y selec ed obse a o y in he a ea. To de e mine he
ep esen a i eness, we calcula ed he p opo ionali y o he a e age annual ain all
be ween he ROA and e e y selec ed s a ion, he R-Pea son coe icien o he annual
o als o he espec i e ain all se ies and he R-Pea son coe icien o he mon hly
a e age o he in a-annual dis ibu ion.
Table 1. P opo ionali y coe icien and annual and in e annual co ela ion be ween he
San Fe nando Obse a o y (ROA) and he selec ed egional s a ions.
Table 1 shows ha al hough he o al ain all di e s among neighbou ing
s a ions and in hose wi hin he same basin, he in a- and in e -annual beha iou is
simila . The high co ela ion o he esul s ob ained in Table 1 shows ha he egion
s udied has he same clima e and is subjec o he same synop ic condi ions. This
co obo a es he conclusions o p e ious s udies on ain all in he sou hwes e n Ibe ian
Peninsula (Ga cía-Ba ón e al., 2011). The e o e, we assume ha he gene al ain all
egime o he ROA su icien ly cha ac e izes he A lan ic sou he n zone o he Ibe ian
Peninsula o analysis o i s empo al a iabili y. Consequen ly, his s udy es ima ed he
beha iou o he empo al e olu ion o he agg essi eness isk using daily ain all
eco ds o he ROA om 1870 o 2010. Absolu e homogenei y es s we e applied o he
annual se ies wi h AnClim so wa e (S epanek, 2007) and he S anda d No mal
Obse a o ies Coun y Ins i u ion La i ude and
Longi ude
Annual
a e age a e
R-Pea son
In e annual
R-Pea son
In a-annual
San Fe nando
(ROA)
Spain ROA
- - -
Cadiz Spain AEMET
1.04 0.96 1.00
Huel a Spain AEMET
1.03 0.94 0.98
Fa o Po ugal IPMA 37° 01' 00" N
7° 55' 59" W
1.04 0.76 0.97
Se ille Spain AEMET
1.02 0.85 0.98
Co do a Spain AEMET
0.96 0.86 0.98
Badajoz Spain AEMET 38° 43 02 N
6° 49 45 W
1.02 0.72 0.94
Beja Po ugal IPMA 38°
0.92 0.70 0.94
Applying equa ion 9 o he espec i e annual alues o IFM* and IPC* o he
en i e s udy pe iod allowed ex apola ion and hus gene a ion o he in e annual
es ima ed se ies o RA om 1870 o 2010. The uni s o RA a e he same as hose o R
[(megajoules
g aphically ep esen s he e olu ion o he annual isk es ima ed o he pe iod 1870-
2010 wi h he co esponding end line.
Figu e 5. Tempo al e olu ion o RA in he SW Ibe ian Peninsula.
Fo he en i e pe iod, he a e age alue, he coe icien o linea end, he Vn
coe icien o a ia ion and he ID gene al dispa i y index o RA we e calcula ed. The
analysis esul s a e shown in Table 2, which also includes he co esponding alues o
he indices IFM*and IPC* o compa ison pu poses.
Table 2. Cha ac e iza ion o he RA and i s compa ison o he espec i e s a is ical
componen s IFM* and IPC*: a e age, end (linea eg ession), explained a iance,
a iabili y and Speci ic Dispa i y Index
A e age T end
2
VN ID
IFM* 21.0 - 0.012 < 0.01 0.28 0.40
IPC* 3.8 < 0.001 < 0.001 0.27 0.35
RA 1742 - 4.63 < 0.1 0.47 0.64

The a e age alue o RA was 1742 uni s. The linea end (Figu e 5) showed a
sligh ly dec easing slope (-4.63 uni / yea ), s a is ically signi ican a he 95% le el (T=
-2.8 <-1.9) bu clima ically no ele an because he explained a iance was lowe han
1% ( 2<0.1). The e o e, he cen al alue was no a su icien p edic o o he empo al
es ima ion o he RA; he high coe icien o a ia ion (VN = 0.47) and he gene al
dispa i y index (ID = 0.64) a e p oo o his s a e. This highligh s he la ge empo a y
luc ua ions o he RA se ies, e en be ween consecu i e yea s. Addi ionally, he
coe icien o a ia ion and he gene al dispa i y index o RA we e highe han hose o
IFM* and IPC*.
Despi e he lack o a signi ican end o RA, i s accumula ed ela i e de ia ions
Ak allowed us o iden i y di e en mul iannual sequences ha cha ac e ized he
in e annual beha iou and, consequen ly, o iden i y sec ions o high and low isk o
agg essi eness.
Figu e 6 ep esen s he accumula ed de ia ions wi h espec o he N a e age o
he whole se ies o RA. An ini ial ups eam line was obse ed un il he end o he
nine een h cen u y and in ol ed a high equency o yea s wi h an agg essi eness isk
highe han he a e age o he se ies. This pe iod o high equency o he
agg essi eness isk coincided wi h he end o he Li le Ice Age in Andalusia, which led
o an impo an clogging and educ ion p ocess in lagoons and small coas al b ooks
(Sousa e al., 2006) in he sou hwes e n Ibe ian Peninsula. Dioda o e al. (2011) no ed
ha e osi e o ces inc eased owa ds he end o he Li le Ice Age (~1850) o e he
wes e n and cen al Medi e anean in gene al and ha e inc eased e en mo e du ing he
ecen wa ming pe iod in me idional Medi e anean egions because o a highe
equency o in ense s o ms. On he o he hand, Figu e 6 shows a downwa d sec ion a
he i s hal o he 20 h cen u y, co esponding o yea s wi h agg essi eness isk below
he a e age and ha coincided wi h a sligh ly d y pe iod wi h smoo h annual ain all
luc ua ions.
Figu e 6. E olu ion o he accumula ed de ia ions wi h espec o he a e age RA.
Finally, a s eep downwa d phase ha we associa e wi h a pe iod o low ain all
agg essi eness s ands ou du ing he las hi y yea s o he 20 h cen u y (Figu e 6). This
phase coincided wi h a d y pe iod in which he e was a g ea e dispe sion o he in a-
annual ain all, a ela i e lack o ain all in sp ing and a shi in ain all owa ds he
au umn mon hs (Ga cía-Ba ón e al., 2013). Da a o he e osion and sil ing o he
halwegs o coas al b ooks in he SW o Spain o his pe iod show lowe ac i i y han
ha o bo h p e iously men ioned pe iods ( he end o he 19 h cen u y and he 1960s o
he 20 h cen u y), which showed high e osi e ac i i y (Figu e 6). Tha is, phases o high
ain all agg essi eness du ing he 19 h and 20 h cen u ies in he SW o Eu ope caused
we land eg ession, especially in lagoons and coas al b ooks (Sousa e al., 2013, 2015).
4.3 Tempo al i egula i y o he es ima ed isk o agg essi eness
The i egula i y o he en i onmen al e ec s caused by ain all o igina es in he annual
and in a-annual ain all i egula i y i sel . In he p e ious sec ions, we discussed he
gene al a iabili y o RA du ing he s udy pe iod by means o VN and ID; consequen ly, i
is necessa y o analyse i s in e annual e olu ion. To do so, we calcula ed he mobile
a ia ion coe icien s o pe iods o ele en yea s (V(11)n) o he n yea s o he se ies
gene a ed (ob iously wi h a educ ion o he i s en elemen s) du ing he obse a ion
pe iod.
The V(11)n a ia ion coe icien associa ed wi h he ime sequence o he RA
annual alue showed peaks o he es ima ed isk in he yea s 1887, 1922, 1961 and 2002
o app oxima ely 0.5, sepa a ed by he co esponding pe iods o minimum alues lowe
han 0.30 (Figu e 7), which indica es highe empo al s abili y o he in e annual RA
alues. This igu e includes he ep esen a ion o he alues end line. The las 25 yea s
o he se ies is cha ac e ized by he g ea es isk a iabili y o he 140 yea s s udied.
Figu e 7 shows a linea end o he coe icien o a ia ion alues wi h a posi i e slope
(y = 0.0009 x +0.387) signi ican o p = 0.05 (TC = 3.62> 1.98), wi h 2 equal o 0.09.
The slope inc eases o 0.015 in he line ha links he ela i e maximum alues (1887,
1922, 1961 and 2002).
Figu e 7. Mobile a ia ion o he RA coe icien o pe iods o ele en yea s wi h he
end line o he en i e pe iod analysed and ha o he maximum ela i e alues.
The e o e, he empo al analysis o RA by means o he V(11)n a ia ion coe icien
shows an almos cyclical pa e n wi h a pulsa ion o app oxima ely 40 yea s (Figu e 7).
This cyclical componen is unique, and we ha e no in o ma ion indica ing ha i had
been p e iously de ec ed in he a iabili y analysis o o he clima e a iables in he
Medi e anean en i onmen . Equi alen esul s we e ob ained by analysing he Speci ic
Dispa i y Index (Idj) a e a ailable in he Suppo ing In o ma ion sec ion (S2). I is also
no ewo hy ha he V(11)n a ia ion coe icien o he RA p esen s a p og essi e inc ease
o i s ela i e ex emes.
5. Discussion
The p oposed me hodology o calcula ing RA was applied o he SW Ibe ian Peninsula.
Tempo al analysis o he gene a ed RA se ies o San Fe nando (ROA, 1870-2010)
showed some sequences o consecu i e yea s ha , as a whole, show a equency o
annual alues highe o lowe han he mean alue. The e was a p edominance o low
agg essi eness du ing he i s hal o he 20 h cen u y, especially du ing he las hi y
yea s; howe e , he e we e peaks o high agg essi eness in he la e 19 h and mid-20 h
cen u ies coinciding wi h pe iods o high soil e osion ha esul ed in sil a ion o lagoons
(Sousa e al., 2013) and b ooks (Sousa e al., 2015) in he sou hwes e n Ibe ian
Peninsula (Biosphe e Rese e o Doñana).
Al hough his s udy was de eloped in he Ibe ian Peninsula, he new pa ame e
is based on IFM and IPC (indices used in di e en edaphic and me eo ological
condi ions), and we conside ha i s applica ion is alid o analysing he po en ial
impac s o ain all in di e en clima ic and geog aphic a eas. Thus, i is necessa y o
de elop a weigh ing local equa ion o bo h indices, (IFM*, IPC*), de e mined by ain all
in each egion.
Se e al s udies (Rena d & F eid, 1994; Dioda o y Bellocchi, 2007; Lee & Heo,
2011; Taguas e al., 2013; Yue e al., 2014) ha e shown a high co ela ion be ween he
R ac o and ain all pa ame e s such as he IFM. Fo hei pa , Michiels e al. (1992)
used he IPC o analyse ain all a iabili y and conside ed ha his index is app op ia e
o e alua ing he e osi i y, and Gab iels e al. (2003) used mon hly p ecipi a ion da a
o analyse he in e annual a iabili y o e osi i y. Apaydin e al. (2006), Elagib (2011),
Elbasi e al. (2013) and Meshesha e al. (2015) used p ocedu es based on hese indices
o analyse e osi i y in a id egions. Based on he IFM, Saue bo n e al. (1999) and
Nea ing (2001) sugges ed he possibili y o changes in he ain all e osi i y in Eu ope
and he USA, espec i ely, du ing he 21s cen u y. De Luis e al. (2010) sepa a ely
applied IFM and IPC o s udy a possible inc ease in e osi i y in he Spanish
Medi e anean a ea. Addi ionally, bo h indices ha e been used o de ec changes in he
empo al end o e osi i y in sou he n Po ugal (Nunes e al., 2016) and, in an
in eg a ed way, analyse he spa ial and empo al a iabili y o agg essi eness in he
wa e sheds o he Ibe ian Peninsula (Ga cía-Ba ón e al., 2015).
The ad an age o he p oposed me hodology is ha i p o ides an accu a e
annual syn hesis pa ame e o di ec in e p e a ion, po en ially applicable o di e en
geog aphical a eas. RA o e comes he limi a ions o he in ensi y models because o he
lack o sub-hou ly eco ds (R ac o ) and he imp ecision o he adi ional olume
models (IFM and IPC) associa ed wi h he e ec s o hea y ain all episodes. The e o e,
he new RA pa ame e is an app op ia e mechanism o es ima ing he po en ial
en i onmen al impac o ain all agg essi eness and o pe o ming spa ial and empo al
compa a i e analysis.
To de e mine he equa ion FM, IPC) wi h su icien accu acy, we needed
minimum simul aneous daily and sub-hou ly ain all eco ds in addi ion o local e osion
da a. An open esea ch line o he u u e is o ex end he applica ion o his
me hodology o o he s udy a eas wi h di e en clima ic condi ions, pa icula ly in he
Medi e anean, semia id en i onmen s and en i onmen s a isk o dese i ica ion, and
o compa e he esul s o he esul s ob ained by o he me hods and a o he ime scales.

Al hough he p oposed me hodology has heo e ical ounda ions, i would be con enien
o es ablish a di ec empi ical e i ica ion o RA o allow o he quan i ica ion o ain all
en i onmen al impac s ( uno , sil a ion o we lands, e c.). Ano he aspec o conside is
ha al hough RA es ima es he ain all po en ial ene gy, he e osi e p ocess is much
mo e complex, and i is no always ha ain all amoun and/o dis ibu ion he main
ac o a ec ing he e osi e p ocess. Ga cía-Ruiz e al. (2015) conduc ed a wo ldwide
me a-analysis o soil e osion a es, based on da a om mo e han 4000 si es, whose
esul s show ha he e is ex ao dina ily high a iabili y in e osion a es, wi h almos
any a e appa en ly possible i espec i e o land slope, clima e, scale, land use/land
co e and o he en i onmen al cha ac e is ics. Despi e his a iabili y, some gene al
ends we e ound, including an inc ease in e osion a es wi h inc easing land slope and
annual p ecipi a ion, he associa ion o ag icul u al p ac ices wi h he highes e osion
a es, and a co ela ion be ween sh ub co e age and he lowes e osion a es. E en so,
he wo ldwide me a-analysis o Ga cía-Ruiz e al. (2005) sugges s ha only o de o
magni ude app oxima ions o e osion a es a e possible. This supposes a high deg ee o
unce ain y and causes hese au ho s o pos ula e he need o de elop p o ocols ha
allow he compa ison o he esul s o di e en si es.
Human ac i i y can also signi ican ly a ec he de elopmen and e olu ion o
denuda ion ho spo s, especially h ough changes in land use (Ve ga i e al., 2013). As
hese au ho s poin ou , his ac o has a g ea impo ance associa ed wi h he c oplands
abandonmen , and in gene al, in badlands o he Medi e anean a ea. The ela ionships
among he a ious ac o s ha in luence he e osion in ensi y a e e y complex, and
he e o e new s udies a e needed o con inue o deepen hese aspec s, wi h he suppo
o eal e osion measu es aken di ec ly om he ield wo k.
6. Conclusions
A new syn hesis pa ame e RA was calcula ed by means o he combined use o he
Fou nie (IFM*) and Oli e concen a ion (IPC*) indices and e o mula ed wi h daily da a.
Weigh ing be ween bo h indices was ob ained by mul iple eg ession wi h he local
e osi i y. The his o ical ex apola ion allowed he in e annual se ies o he RA o be
ob ained. A compa a i e analysis o he empo al e olu ion o IFM* and IPC* showed ha
hey we e independen o each o he and ha hei con ibu ions o he calcula ion o RA
we e complemen a y. Ob aining he annual alues o RA in he same uni s and scale as
he USLE R unc ion allowed o he gene aliza ion o he esul s, hus inc easing hei
applicabili y and es ablishing a link among his o ical ain all eco ds and cu en alues
o he po en ial ain all agg essi eness.
In ou opinion, he p oposed me hodology has he abili y o p o ide consis en
conclusions abou his o ical e osi e p ocesses in each egion linked o he po en ial
ain all agg essi eness. The e o e, i has a special ele ance o he design o
en i onmen al measu es and land managemen policies ha p e en he di ec and
indi ec impac s o ain all.
7. Acknowledgemen s
p o iding he ain all eco ds and he En i onmen al In o ma ion Ne wo k o he
Minis y o En i onmen o he Jun a de Andalucía o p o iding he da a se o
calcula e he e osi i y. We hank Ma ía Ángeles Ga ido and Alicia Cebolla o hei
help in da a p ocessing.
8. Re e ences
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116. h ps://idus.us.es/xmlui/handle/11441/30483
Alexande sson H. 1986. A homogenei y es applied o p ecipi a ion da a. Jou nal o
Clima ology 6: 661- 675. DOI:10.1002/joc.3370060607.
Alma za C, López A, Flo es C. 1996. Homogeneidad y a iabilidad de los egis os
his ó icos de p ecipi ación en España. Ins i u o Nacional de Me eo ología,
Mad id.
Angulo-Ma ínez M, López-Vicen e M, Vicen e-Se ano SM, Begue ía S. 2009.
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me hods in he Eb o Basin (NE Spain). Hyd ology and Ea h Sys em Sciences
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cha ac e izing he dis ibu ion and concen a ion o p ecipi a ion: a case o he
egion o Sou heas e n Ana olia P ojec , Tu key. Jou nal o Hyd ology 328:
726-732. DOI:10.1016/j.jhyd ol.2006.01.019.
A noldus HMJ. 1980. An app oxima ion o he ain all ac o in he uni e sal soil loss
equa ion. In: Assessmen o E osion, De Bood M, Gab iels D (eds). John Wiley:
Chiches e ; 127-132.
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he Medi e anean Ibe ian Peninsula? Land Deg ada ion & De elopmen 21:
139-144. DOI:10.1002/ld .918.
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DOI:10.1016/j.jhyd ol.2007.08.008.
Dioda o N, Cecca elli M, Bellocchi G. 2008. Decadal and cen u y long changes in he
econs uc ion o e osi e ain all anomalies in a Medi e anean lu ial basin.
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Elagib NA. 2011. Changing ain all, seasonali y and e osi i y in he hype -a id zone o
Sudan. Land Deg ada ion & De elopmen 22: 505 512. DOI:10.1002/ld .1023.
Elbasi AMA, Ojha CSP, Jinbai H, Yasuda H, Kimu a R, Ahmed Z. 2013. Rela ionship
be ween ain all e osi i y indica o s unde a id en i onmen s: Case o
Liudaogou basin in Chinese Loess Pla eau. Jou nal o Food, Ag icul u e &
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issue_2/2013-issue_2-en i onmen /e55.pd .
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Gab iels D, Ve meulen A, Ve bis K, Van Mei enne M. 2003. Assessmen o ain
e osi i y and p ecipi a ion concen a ion in Eu ope. In: P oceedings o he
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Table 1. P opo ionali y coe icien and annual and in e annual co ela ion be ween he
San Fe nando Obse a o y (ROA) and he selec ed egional s a ions
Obse a o ies Coun y Ins i u ion La i ude and
Longi ude
Annual
a e age a e
R-Pea son
In e annual
R-Pea son
In a-annual
San Fe nando
(ROA)
Spain ROA
- - -
Cadiz Spain AEMET
1.04 0.96 1.00
Huel a Spain AEMET
1.03 0.94 0.98
Fa o Po ugal IPMA 37° 01' 00" N
7° 55' 59" W
1.04 0.76 0.97
Se ille Spain AEMET
1.02 0.85 0.98
Co do a Spain AEMET
0.96 0.86 0.98
Badajoz Spain AEMET 38° 43 02 N
6° 49 45 W
1.02 0.72 0.94
Beja Po ugal IPMA
0.92 0.70 0.94

Table 2. Cha ac e iza ion o he RA and i s compa ison o he espec i e s a is ical
componen s IFM* and IPC*: a e age, end (linea eg ession), explained a iance,
a iabili y and Speci ic Dispa i y Index
A e age T end
2
VN ID
IFM* 21.0 - 0.012 < 0.01 0.28 0.40
IPC* 3.8 < 0.001 < 0.001 0.27 0.35
RA 1742 - 4.63 < 0.1 0.47 0.64
FIGURE LEGEND
Figu e 1. Map showing he loca ions o he me eo ological s a ions used in he s udy
a ea.
Figu e 2.a) Tempo al e olu ion o he IFM* and b) he IPC* showing he a e age alue
and mobile a e age o pe iods o ele en yea s.
Figu e 3. Pai wise sca e plo o he ime se ies IFM* and IPC* o he pe iod 1870-2010.
Figu e 4. Pai wise sca e plo o he USLE R ac o and he RA ime se ies o he pe iod
1991-2010.
Figu e 5. Tempo al e olu ion o RA in he SW Ibe ian Peninsula.
Figu e 6. E olu ion o he accumula ed de ia ions wi h espec o he a e age RA.
Figu e 7. Mobile a ia ion o he RA coe icien o pe iods o ele en yea s wi h he
end line o he en i e pe iod analysed and ha o he maximum ela i e alues.