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17
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
DOI: 10.4408/IJEGE.2015-01.O-02
L
uca
Milanesi
(*)
, M
arco
Pilotti
(*)
, a
Lberto
CleriCi
(*)
& Z
oran
GavriloviC
(**)
(*)
Università degli Studi di Brescia - DICATAM - Via Branze, 43 - 25123 Brescia, Italy
E-mail: luca.milanesi@unibs.it - marco.pilotti@unibs.it - alberto.clerici@unibs.it
(**)
Institute for the Development of Water Resources “Jaroslav Černi” - Jaroslava Černog, 80 - 11226 Beograd, Serbia - E-mail: gavrilovicz@sbb.rs
APPLICATION OF AN IMPROVED VERSION
OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
la valutazione dei processi erosivi e delle loro conseguenze riveste un ruolo fondamentale nella corretta gestione del territorio;
gli ambiti d’interesse sono relativi alla fruibilità del suolo, inteso come risorsa ambientale ed economica, all’assetto idrogeologico e,
non da ultimo, alle interazioni con numerose opere di ingegneria tra cui spiccano gli invasi ed i manufatti di derivazione. Per queste
ragioni si rivelano di grande interesse applicativo le metodologie per la stima del contributo solido di un bacino idrografico ad oppor-
tune scale spaziali e temporali.
nel presente contributo si considera un modello empirico, il Metodo dell’erosione Potenziale (G
avriLovic
, 1988), che fornisce indi-
cazioni a scala annua sul volume di suolo eroso e trasportato alla sezione di chiusura di un bacino. si propone una revisione organica di
alcuni dei suoi criteri di parametrizzazione e delle modalità di implementazione. in particolare, al fine di garantire maggiore semplicità
ed oggettività alla fase di stima dei valori dei parametri sul bacino, si è inteso riconsiderare le modalità di classificazione dell’uso del
suolo e delle caratteristiche geomeccaniche dei terreni e delle rocce tramite schemi largamente diffusi nella comunità scientifica (e.g.,
Corine 2000 per la descrizione degli usi del suolo). si propone inoltre di limitare il periodo d’applicazione, originariamente a scala
annua, ai soli periodi in cui le temperature, le caratteristiche delle precipitazioni e le portate sono tali da garantire l’effettivo innesco dei
processi di erosione ed il trasporto del materiale nei corsi d’acqua. Questo approccio permette quindi di superare alcune difficoltà legate
alla soluzione delle equazioni che compongono il modello estendendone quindi l’applicabilità anche a zone con temperatura media an-
nua negativa, che caratterizzano ad esempio i bacini alpini d’alta quota. applicando il modello sia secondo la metodologia originaria che
implementando le modifiche proposte, sì è potuto osservare che queste non alterano le stime di produzione di sedimento ma aumentano
significativamente l’oggettività dei risultati e la semplicità di applicazione dello schema.
si propone inoltre una analisi statistica sull’opportunità dell’applicazione del modello in forma distribuita piuttosto che a parametri
concentrati. sebbene l’applicazione a parametri concentrati risulti generalmente più semplice, l’implementazione distribuita del mo-
dello tramite opportuni codici di calcolo permette di cogliere maggiormente le specificità locali del bacino; le differenze conseguenti ai
due diversi approcci metodologici possono raggiungere il 14%. si è infine testata l’effettiva applicabilità del modello e delle modifiche
proposte in ambiente alpino, per il quale esso non era stato originariamente derivato. il modello è stato applicato in forma distribuita a
31 bacini in alta valtellina (sondrio - italia) le cui acque sono convogliate per lo sfruttamento idroelettrico negli invasi di san Giacomo
di Fraele, Cancano e val Grosina. sulla base delle informazioni fornite dal gestore degli impianti, è stato possibile ricostruire il volume
di sedimento, quasi esclusivamente composto da limo glaciale, attualmente raccolto negli invasi dopo circa 50 anni di esercizio. al fine
di rendere omogenee le stime del modello, che comprendono l’intero spettro granulometrico, e le informazioni di interrimento dei baci-
ni, che invece riguardano la sola frazione fine, si è provveduto ad eseguire una serie di campionamenti dei terreni dei bacini studiati ed
effettuare analisi granulometriche volte a definire la percentuale di materiale fine che costituisce i sedimenti. tramite questa procedura
è stato quindi possibile stimare il volume di materiale fine che annualmente viene eroso in ciascun bacino e convogliato in sospensione
nei corsi d’acqua fino agli invasi e confrontare positivamente le informazioni di interrimento con i risultati del modello.
in conclusione, questo studio propone modifiche sostanziali nelle tabelle e nelle modalità di implementazione del modello senza
influire tuttavia sulle relazioni, sulle ipotesi di base e sui risultati. la fase applicativa mostra che le stime fornite dal metodo, sebbene
affette da significative soglie di incertezza peraltro insite in questo tipo di fenomeni, sono sostanzialmente in buon accordo con le os-
servazioni di lungo periodo sull’interrimento dei serbatoi.
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L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
18
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
AbSTRACT
the assessment of erosive processes is of great importance
in environmental engineering, resource management and land
planning. in this paper the empirical approach known as erosion
Potential Method (EPM) was improved to simplify the identifi-
cation of the involved parameters. in addition, EPM suitability
for alpine watersheds, where the average yearly temperature may
be below 0°C, was discussed. the advantages of distributed ap-
proaches rather than lumped methodologies were tested. EPM
was then implemented in a distributed form for a set of 31 catch-
ments located in alta valtellina (northern italy) in order to cap-
ture the spatial variability of the parameters and the intensity of
the erosion processes. the results obtained for these catchments
were positively compared to long-term sedimentation data from
three reservoirs and from a turbidimetric station.
K
ey
words
: erosion potential method, soil erosion, Alpine reservoirs se-
dimentation
INTRODuCTION
sediment supply of rivers is a consequence of a wide set of
distributed erosion phenomena acting in a watershed. the evolu-
tion of such processes might be slow (e.g., freeze-thaw action
and growth of plant root system in rock joints, chemical weath-
ering processes like hydrolysis and oxidation) or characterized
by a greater velocity (e.g., soil creep, rill and gully erosion) and
even by a very high velocity (e.g., some kind of landslides, debris
flows). as a result, the volume of involved materials might be
relevant and the effects are usually of primary importance both in
the field of environmental engineering and of agriculture. it has
been reckoned that almost 1.2 kg/m
2
of soil per years are lost in
intensive agriculture areas in the Usa as a consequence of wa-
ter and wind erosive capacity (u.S. D
epartMent
of
a
GricuLture
,
2009). in addition, sediments are an important source of pollu-
tion for water bodies both in terms of turbidity and of nutrients.
Finally, the settling of sediments in reservoir may cause important
related problems, such as the reduction of their storage capacity
(v
anoni
, 1975), damages to electromechanical machinery (pipes
and turbines) and potential impairment of the properties of drink-
ing water. For instance, about 30% of the original italian storage
volume is now occupied by sediments (itColD, 2009) and this
fraction is about 35% worldwide (b
aSSon
, 2010).
the importance of the consequences of soil erosion prompts
continuous research for effective methodologies to quantify soil
loss in catchments. to this purpose, different approaches might
be identified in the literature. Hydraulic modelling focuses on
the transport capacity of the river through the calibration of sedi-
ment transport formulae at the local level. these relations are
generally obtained through laboratory experiments under the hy-
pothesis of infinite sediment availability, steady, two-dimension-
al and uniform flow (e.g., G
raf
, 1971; Y
aLin
, 1977; r
auDkivi
& t
an
, 1984; S
iMonS
& S
entürk
, 1992). the distribution of the
suspended fraction is usually computed through additional con-
siderations about turbulence and sediment concentration along
the vertical direction. From this point of view, the estimate of
the mean annual sediment transport volume may be performed
by time integration using the flow duration curve of the studied
stream. a possible criticism to this approach regards the inter-
mittency of the actual sediment transport, which, also in steady
flow conditions, is controlled by the sediment availability and is
triggered by intense hydrologic events. this is particularly true
in mountain areas, where most of the sediment production occurs
during few strong events because of the strengthened carrying
capacity of the flow and the increased availability of sediments
into the streambed (e.g. p
itLick
& t
horne
, 1987). accordingly,
conceptualized approaches to assess the overall relevance of
sediment production at the basin scale are justified.
the catchment-wide soil erosion models available in the lit-
erature can be classified according to their conceptual features
and different space and time scales of application (e.g.,
De
v
ente
& p
oeSen
, 2005). Moreover, some of these models were devised
to estimate soil loss for specific purposes only (e.g., agricultural
conservation) while others have a wider scope, with possible
applications in land planning, river restoration and reservoir
management. the choice of the most suitable model depends on
the goal of the application, on the reliability of the model for
the specific morpho-climatic environment (e.g., arid/semi arid
landscapes, mountainous regions, agricultural lands) and finally
on the available data. Physically based, conceptual and empiri-
cal methodologies can be found in the literature (e.g. M
erritt
et alii, 2003). Physically based models provide a mechanistic
description of erosive processes through fundamental conserva-
tion principles and constitutive equations. these methods assess
the interaction of each element and return the variation of sedi-
ment production in space and time, usually requiring a consider-
able amount of input data and of computational effort (r
anZi
et alii, 2012). among others, the widespread models CreaMs,
Kineros, eUroseM, liseM and WePP might be cited (e.g.,
n
earinG
et alii, 1989; D
e
r
oo
et alii, 1995; S
Mith
et alii, 1995;
b
raZier
et alii, 2000). Conceptual models may be regarded as
a compromise between empirical and physically based models
because they link conservation equations to empirical relation-
ships. Finally, empirical formulae describe the phenomena in a
simplified way through regressive relations of experimental data
that link together the most statistically relevant parameters. Due
to their simplicity, the use of empirical methodologies is widely
documented in the literature. indeed, despite a simple formal
structure, they usually provide a valuable engineering approach
to soil erosion estimate if used into the same geomorphological
environment where they were calibrated. among others the fol-
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
19
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
lowing models might be cited: Usle and further revisions for
agricultural areas (W
iSchMeier
& S
Mith
, 1978); PsiaC for arid
and semi arid regions; denudation index based on geomorphic
parameters for badlands (e.g., D
eLLa
S
eta
et alii, 2009).
among empirical methodologies, the erosion Potential
Method (G
avriLovic
, 1988), in the following also indicated as
EPM”, is a semi-distributed model for the estimation of the
mean annual soil erosion and sediment yield at the basin scale.
Despite its original formulation, applications at a smaller time
step can be found in the literature (e.g., b
eMporaD
et alii, 1997)
as well as space-distributed implementations that better account
for the local variability of the involved parameters (D
e
c
eSare
et
alii, 1998; e
MManouLouDiS
et alii, 2003; G
Lobevnik
et alii, 2003;
t
anGeStani
, 2006; b
oZorGZaDeh
& k
aMani
, 2012; b
aGherZaDeh
& D
aneShvar
, 2010). these improvements take advantage of the
development of digital cartography and Gis technologies.
although EPM was calibrated using laboratory and field
data for the Dinaric alps, several literature contributions test the
applicability of EPM in different climatic areas. For instance,
several researches assess the suitability of EPM to semiarid
Mediterranean regions (e.g., e
MManouLouDiS
et alii, 2003; e
M
-
ManouLouDiS
& k
aikiS
, 2006; t
anGeStani
, 2006; S
oLaiMani
et
alii, 2009; b
oZorGZaDeh
& k
aMani
, 2012) and to the alpine and
appenninic area (e.g., p
oZZi
et alii, 1990; M
ikoš
et alii, 2006;
f
anetti
& v
eZZoLi
, 2007; t
aZioLi
, 2009; Z
orn
& k
oMac
, 2009).
anyway, the original form of EPM cannot be applied in areas
characterized by mean annual temperature below -1°C because
of the definition of the temperature coefficient.
another major stumbling block that hinders the widespread
application of EPM arises from its parameterization tables,
whose original definitions are sometimes of difficult interpre-
tation and generalization. Hence, the reliability of the results
might be significantly affected by the user’s experience. to limit
these effects, improving the reliability of the results and reduc-
ing the influence of users’ know-how, many authors suggested
modifications to the EPM tables (S
tefanović
et alii, 2010; b
o
-
ZorGZaDeh
& k
aMani
, 2012; t
oSic
& D
raGicevic
, 2012). How-
ever these efforts have not delivered a complete and easy-to-use
revision of the original classification.
this paper deals with these limitations of EPM: the model was
applied to a cold alpine environment by suggesting a modification
of the original temperature parameter and the classification tables
were revised on the basis of widespread classification methodolo-
gies (e.g. Corine land Cover for land use factor). this greatly sim-
plifies the application of the model by increasing the objectivity of
parameters definition. Moreover, a procedure for the distributed ap-
plication of the methodology is presented and its actual advantages
are briefly discussed. the model was applied to 31 alpine catch-
ments in alta valtellina (northern italy) and the results were posi-
tively compared to measured sedimentation and turbidimetric data.
THE EROSION POTENTIAL METHOD
EPM is an empirical formula that supplies the mean annual vol-
ume of sediments eroded and the fraction yielded to the outlet of a
river basin. erosive phenomena arise from the interaction of litho-
logical, topographic, climatic and land use quantities (e.g., f
ournier
,
1960; M
orGan
, 1979) that in this model are linked by the relation:
where W
sp
(m
3
/km
2
) is the specific mean annual production of
sediment and P (mm) represents the mean annual cumulative
rainfall. With reference to the latter, Z
orn
& k
oMac
(2009) high-
lighted some modifications introducing the maximum daily rain-
fall in order to make the model able to account also for extreme
events which otherwise would not be considered (e.g., M
ikoš
et
alii, 2006). the temperature coefficient t (-) is calculated as:
where t (°C) represents the mean annual temperature. the param-
eter Z (-) is defined as:
where X (-) describes the protection by vegetal or artificial cover-
age against erosive factors and is a function of land use; Y (-) rep-
resents soil resistance against water erosive capacity and is a func-
tion of the basin lithological and pedologic features; φ (-) indicates
the intensity of the active erosion processes; i (m/m) is the mean
slope of the investigated area, that can be calculated through an
area-weighted average. the mean annual sediment yield G (m
3
/y)
at the outlet accounts for the actual transport capacity of the flow:
G
=
W · R
=
W
sp
· F · R
where the retention coefficient R (-) represents the percentage of
sediments that reaches the outlet, W (m
3
/y) is the volume of erod-
ed sediment and F (km
2
) the area of the river-basin. accordingly,
eq. (4) reflects the possible reduction of transported sediments
along the watercourse due to the local decrease of bed shear
stress. G
avriLovic
(1988) suggested to compute R as:
where O (km) is the perimeter of the catchment, ΔĤ (km) the
mean geodetic relief and L (km) the linear dimension of the catch-
ment along the main channel. on the basis of further studies in al-
pine areas, Z
eMLjic
(1971) observed that eq. (5) tends to overrate
the effective ratio between eroded and yielded sediments. some-
times it may even return unphysical values larger than 1. Hence,
Z
eMLjic
(1971) suggested the following relation:
where Ĥ (km) indicates the mean altitude of the basin and L
i
(km)
represents the length of i
th
order channels. equation (6) was used
in this paper.
(1)
(2)
(3)
(4)
(5)
(6)
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L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
20
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
IMPROVEMENTS TO EPM
in this section some modifications to EPM are proposed in
order to cope with the problems arising in the identification of
its parameters and in the application in cold mountain areas. the
application of eq. (2) in alpine areas with mean annual tempera-
ture below -1 °C, is not possible because of the negative value
of the radical. However, in these areas, erosion processes are
mostly concentrated in the period from spring to fall, (e.g., D
e
c
eSare
et alii, 1998), because in winter period both the soil and
the streams are usually frozen and the snow precipitations have
no erosive power. indeed, although freeze-thawing cycles gen-
erate sediments and snow avalanches might convey significant
amount of sediments only if the sliding plane coincide with the
soil layer, in average terms the most effective sediment trans-
port processes are related to rainfall and stream waters. accord-
ingly, it seems reasonable to apply EPM during the active ero-
sion period only, computing the averaged temperature and the
cumulative rainfall on such temporal window instead of using
Tab. 1 - Values of the land cover parameter X
* Glaciers and perpetual snow, although protecting soil against rainfall erosivity, exert a relevant erosive action due to meltwaters. Accordingly, in
order to cope with this ambiguity, these elements are associated to the maximum value of X, that would mean the lowest protection against erosion
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
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Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
the mean annual values. in this way it is possible to apply EPM
also in regions characterized by periods with average tempera-
ture below zero.
in order to simplify the assessment of EPM coefficients in
eq. (3), reducing ambiguities in the parametric description of the
catchment, we propose a systematic correspondence between the
original classification tables and some widespread classification
systems of land use, geology and active erosion processes. this
task was already attempted to a more limited extent by other re-
searchers (e.g., e
MManouLouDiS
et alii, 2003; G
Lobevnik
et alii,
2003; f
anetti
& v
eZZoLi
, 2007), who related the original EPM
classification table of the parameter X to the Corine Land Cover
classes (eea, 2000). the Corine Land Cover system represents
a reference point at the european level and its maps are freely
available in digital format on the web, fostering space-distributed
GIS applications.
the analysis of the analogies between the elements of the
original parameterization by G
avriLovic
(1988) and Z
eMLjic
(1971) and the categories of the Corine Land Cover system sug-
gests the correspondence proposed in tab. 1.
the coefficient Y describes soil erodibility as a function of
rock and soil properties (tab. 2). the main goal of the re-classifi-
cation of this parameter is to substitute the original classification,
where geological and geomorphological characteristics of the de-
posits were mixed together, with a more systematic one where
soils and rocks are divided in two distinct categories. soils are
classified on the basis of the particles size and rocks are subdi-
vided according to their mean mechanical characteristics.
the parameter φ, describing the intensity of the active erosion
processes, can be calculated by two distinct procedures. the first
approach is based on the general overview of the study area and
returns a measurement of the intensity of erosion processes at the
river basin scale. this study provides a simplified subdivision and
includes some intensive erosion landforms not comprised in the
original classification tables (tab. 3).
alternately, a more detailed approach for the assessment of φ
goes through the V/F ratio, where V is defined as:
where F
i%
(-) represents the percent area covered by the i
th
ero-
sion landform and F
i
(km
2
) indicates the surface covered by the
i
th
erosion landform. the weight of each erosive type, P
i
(-), is
given in tab. 4. the parameter φ is finally provided by tab. 5 as
a function of the ratio V/F.
VALIDATION OF THE MODIFIED VERSION OF EPM
in order to compare the improved and the original EPM for-
mulations, they were both tested in two small alpine catchments
in alta valtellina (northern italy) using a lumped approach. al-
though the most effective comparison would have been with re-
spect to the same environment of calibration of EPM, the model
was partly calibrated using laboratory tests and experimental
plots, so that the original data are not relevant for implementation
at the basin scale. Moreover, tests in the Dinaric alps would not
allow to verify the effect of the modifications provided to cope
with negative temperatures.
Tab. 2 - Values of the erodibility parameter Y
* In order to avoid excessive refinement of the classification, fine soils are grouped in a single class although it is well known that clayey soils are
less erodible than sandy ones. Accordingly higher values of Y are associated to sand and prevailing sandy soils
(7)
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L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
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Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
the first test case regards val Cancano, a small catchment
(3.8 km
2
) on the left side of the Cancano reservoir (Fig. 1). the
input data and the results provided by the original methodology,
based on Z
eMLjic
(1971) tables, were obtained by Q
uintavaLLe
(2004). it is important to remark that the study by Q
uintavaLLe
(2004) used a parameterization based on yearly averaged quanti-
ties, while the current study is based on the modified formulation,
that makes use of the cumulative precipitation and of the aver-
age temperature for the period (from May to october) when the
average temperature is positive. as shown in tab. 6, the results
obtained from the two different formulations of EPM are in good
agreement. accordingly, it is possible to state that the new param-
eterization and the introduced variations on thermal and rainfall
coefficients have no relevant effects on the results but simplify
the applicability of the model, widening its scope to cold regions.
the relevant difference on the active erosion coefficient might
be partly explained by considering that we applied the procedure
based on eq. (7), while Q
uintavaLLe
(2004) used tab. 3.
the second test case regards the Cedec creek basin (Fig. 1)
and focuses only on the effect of the introduced variations to the
parameterization tables. this watershed has an area of 17.3 km
2
and a mean slope of 42.5%. the results obtained with the modi-
Tab. 4 - Values of the parameter P
i
describing the active erosive proc-
esses in the catchment
Tab. 5 - Values of the parameter φ describing the active erosion proc-
esses in the basin
Tab. 3 - Values of the parameter φ describing the active erosion processes in the basin
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
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Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
fied EPM were compared with those by b
aSSi
(2000), obtained
on the basis of Z
eMLjic
(1971) tables, in order to test the influence
of the modified tables only. in order to obtain fully comparable
results independent from the extent of the simulation period, we
used the same average yearly temperature and cumulative pre-
cipitation (1145 mm) introduced by Bassi. in order to cope with
the negative value of the radical in eq. (2) in a situation where the
actual average yearly temperature of the basin would be -1.3°C,
b
aSSi
set this value to 0°C. Moreover, he considered X equal to
0 for the glacier area, a low value that would reflect the protec-
tion exerted by ice to soil and rocks. although the erosive effect
usually exerted by glacial meltwaters could lead to much higher
values of X (see also tab. 1), in this test case we assumed a ficti-
tiously low value of X for glaciers as done by b
aSSi
, in order to
keep constant this term of the problem and obtain directly com-
parable results. Finally, one could observe that this assumption
lead to an underestimation of the sediment volume since the role
of glaciers is completely neglected. tab. 7 shows that the results
provided by the modified version of EPM approximate properly
the ones based on the original classification tables. indeed, in this
kind of complex problem covering a large basin, a 20% error in
the evaluation of sediment volume might be regarded as a good
Fig. 1 - The alpine catchments considered in this paper
Tab. 6 - Parameters and results for the Val Cancano test case, according to the original and the modified EPM versions
Tab. 7 - Comparison of input data and results for the Cedec catchment
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L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
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Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
result, although the lack of literature data (e.g., b
oarDMan
, 2006)
does not allow statistical analyses and confirmations. Hence, the
modified parameterization tables do not affect significantly the
results of the original procedure and simplify the application of
the model, fostering its automated implementation.
COMPARISON bETwEEN LuMPED AND DISTRI-
buTED MODELLING OF EPM
the spatial scale of application of erosion models is a rel-
evant aspect that controls the physical meaning of the input data
and, accordingly, the quality of the results. in particular, there is
often the need to preserve the original spatial distribution of the
parameters at the slope (parcel) scale (in the order of 10
3
m
2
),
while providing results at the basin scale (in the order of 10
6
m
2
).
in a strongly non-linear process like sediment erosion, there is no
guarantee that the use of space-averaged parameters leads to an
outcome similar to that provided by the space averaging of the re-
sults obtained at the local scale. in addition, the averaged param-
eters at the basin scale may lose their original physical meaning.
the EPM parameters were defined through parcel observa-
tions (G
avriLovic
, 1988), but its practical application is often
for large catchments (e.g., G
avriLovic
, 1988; e
MManouLouDiS
et
alii, 2003; t
aZioLi
, 2009). in order to find a compromise between
these two scales, EPM is usually applied in a semi-distributed
fashion, according to which the catchment is subdivided into geo-
morphologically and climatologically homogeneous units. in this
direction, the use of automated computational procedures, along
with geomorphological surveys, is mandatory and in the follow-
ing we shall make use of the geomorphological information con-
tained within the space filling drainage network of a basin to deal
with EPM computation.
Considering the control exerted by the topography on the
movement of water within a catchment, it is not surprising that
over the last decades a great effort has been done to couple
quantitative geomorphology and hydrology. in this perspective
the use of Digital terrain Models (DTM) has become a well es-
tablished practice for the extraction of topologic and geomor-
phological information. typically, DTM have been used for the
computerized extraction of the connected space filling drainage
network (SFDN) and of the channel network (CN). the first one
is the set of all local flow directions for the physically based
simulation of runoff processes and the second one is the sub-
set of
SFDN where free surface flow takes place, to be used for
flood routing within a river basin. Considering that both bedload
and washload depend on water erosive and transport capacity,
which are a function of local properties (e.g., the local slope) but
also of integrative properties of the locally drained catchment,
as already proposed by c
iccacci
et alii (1986), p
iLotti
& b
acchi
(1997) computed the sediment yield from a catchment exploiting
the informative content of SFDN and CN.
the scale gap between parcel and basin information can be
filled by taking advantage of the powerful reorganization of the
DTM informative content accomplished by the SFDN and the CN
as described by p
iLotti
et alii (1996). to this purpose, an exten-
sive automatic DTM pre-processing can be used, in order to filter
depressions and flat areas that would prevent the identification of
the drainage network. then, using this enhanced information, the
steepest directions can be identified and the SFDN derived. By
filtering the SFDN on the basis either of a fixed threshold contrib-
uting area principle (o’c
aLLaGhan
& M
ark
, 1984; b
anD
, 1986,
1993) or of a slope dependent critical support area (M
ontGoMerY
& D
ietrich
, 1992; M
ontGoMerY
& f
oufuLa
-G
eorGiou
, 1993), the
CN can be extracted (Fig. 2). Finally, the hillslope drainage net-
work is obtained by logical subtraction of the CN from the SFDN.
the networks allow a complete reorganization of the infor-
mation contained within the DTM, using non-binary logical tree
structures that can be effectively explored by so-called “visiting”
recursive algorithms. the use of such procedures allows to com-
pute locally eq. (1), moving from link to link within the SFDN
and following the same order that would be followed by runoff
on the terrain. at each cell, these algorithms operate on data com-
puted locally from the DTM (e.g., local slope and temperature)
and on raster data made available by the user (e.g., soil properties
and land use). at the same time, they take memory of the integra-
tive properties that are a function of the upstream explored cells
(e.g., the local discharge or the overall drained area).
in order to test the advantages of distributed versus lumped
approaches in this problem, a set of seven basins, with area F
ranging from 1 to 110 km
2
and described by a DTM of constant
Fig. 2 - The cumulative EPM sedimentogram, computed in a distrib-
uted fashion along the drainage network, is represented on
the DTM and then superimposed to the Space Filling Drain-
age Network (SFDN; thin solid lines) and Channel Network
(CN; thick solid lines)
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
25
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
cell size of 20 m, were studied. the parameters X, Y, φ and i
were assumed to be randomly distributed in space according to
a normal distribution law. after computing the average param-
eter values, EPM was applied in both lumped and distributed
forms. the percentage variations Δ between the results obtained
from the two approaches were computed, progressively increas-
ing the variation coefficients CV of the parameter distributions.
the analysis were repeated for each parameter keeping the oth-
ers constant to their mean value μ. since the variation of these
parameters (except the local slope i) is set by EPM tables in lim-
ited ranges (e.g. 0-1 or 0-2), the mean value and the maximum
standard deviation of the distributions were limited to keep at
least 96% of the values within these ranges. in case of param-
eters generated outside of their definition range, their value was
reset to the closest acceptable value.
tab. 8 and Fig. 3 show the tested CV ranges and the aver-
age computed variation Δ for the seven cases. the results high-
lighted a substantial independency of Δ with respect to the area
of the catchment. in real applications all the parameters change
simultaneously so that, in this case, the value of Δ might in-
crease up to 14%.
although in the following we applied EPM will be applied
in a distributed fashion, the small difference between the results
obtained operating in a distributed and lumped way shows that
the EPM is sufficiently robust to provide fairly reliable results
also in lumped applications. the advantages of a distributed ap-
plication mostly lie in the possibility to preserve the physical
meaning of the parameters and in the possibility to identify the
most productive areas within the catchment, as shown in Fig. 2
where the cumulative sediment production along the drainage
network is shown.
APPLICATION TO ALPINE CATCHMENTS AND
RESuLTS
in order to test the reliability of EPM estimates, the results
of a distributed application on 31 catchments in alta valtellina,
northern italy (tab. 9 and Fig. 1), were compared to the meas-
ured data of long term reservoir sedimentation and turbidity.
the study area, located in the retic alps, is drained by the
adda river and is a part of the austro-alpine geological domain
which is constituted by a complex series of allochthonous units
(overthrusts and nappes) which overlapped each other’s during
the alpine orogenesis. Within such units, both crystalline (phyl-
lite and gneiss) and sedimentary (triassic and Jurassic lime-
stones) formations are present. From a geomorphological per-
spective, periglacial and glacial landforms are combined with
gravitative and water erosional elements. the mean cumulative
precipitation of this area is about 880 mm/y, mainly concen-
trated during the period from May to october (590 mm). Most
of the catchments surface is covered by natural vegetation with
different levels of protection (e.g., forests, pastures, etc.) whilst
35% of the surface is characterized by bare rocks and sediments.
only 4% of the whole area in the east side of the investigated
region is occupied by glaciers.
in order to perform a distributed application of EPM, the al-
gorithm proposed by p
iLotti
& b
acchi
(1997) was modified to
compute locally eq. (1), through a recursive visiting algorithm
that explores the SFDN (Fig. 2). the cumulative sediment yield
G was finally obtained by multiplying the sediment production at
the outlet W by the retention coefficient R from eq. (6). the local
slope maps were automatically calculated during the identifica-
tion of the steepest descent directions from the DTM with cell
size 20 m. the raster input data files of erodibility, land use and
precipitation were automatically associated by the software to the
corresponding cells of the SFDN. the input data were derived
both from the literature (e.g., p
oZZi
et alii, 1990) and from digital
information made available by regione lombardia: on the basis
Tab. 8 - Average variation Δ of sedi-
ment production between
distributed and lumped ap-
plications of EPM
Fig. 3 - Average variation Δ of sediment production between distrib-
uted and lumped approaches as a function of the variation co-
efficient CV
background image
L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
26
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
of these data, the values of the EPM parameters were selected
using the modified tables proposed in section 3. the hydro-mete-
orological quantities referred to the period from May to october
were calculated using a 15 years dataset of daily recorded tem-
perature and precipitation in 14 stations located within the study
area. the local temperature in each cell was calculated as a linear
function of the cell elevation, considering an altitude gradient of
-0.004 °C/m. on the contrary, precipitation was assumed constant
on the basin (see also D
e
c
eSare
et alii, 1998). according to the
approach based on eq. (7), the active erosion processes parameter
was assumed constant at the basin scale (see also D
e
c
eSare
et
alii, 1998). indeed, although erosive processes are diffused on the
basin and their influence should be compute in a distribute form,
no procedures that allow to consider the distributed influence of
active erosion processes is available in EPM.
the 31 catchments are linked for hydropower purposes to the
san Giacomo, Cancano and val Grosina reservoirs (Fig. 1) and
can be subdivided into 3 main groups: “Forni”, “spöl” and “val
Grosina” (Fig. 4). the “Forni” and “spöl” groups are connected
through a diversion canal to the san Giacomo reservoir; the “val
Grosina” group delivers its water to the dam of val Grosina by a
different diversion canal. the reservoir of san Giacomo is just
upstream of the Cancano reservoir, so that water and suspended
sediments flow from the san Giacomo to the Cancano reservoir.
Finally, the Cancano reservoir is connected for daily regulation
purposes to the val Grosina reservoir.
the computed mean sediment yield of each group of catch-
ments (tabs. 9 and 10) was compared to the sedimentation meas-
urements of their reference reservoirs. in particular, the results
of the “Forni” and “spöl” groups were related to the amount of
sediment estimated by bathymetric surveys in the san Giacomo
and Cancano reservoirs. as a matter of fact, these two reservoirs
are set in series and, according to the reservoirs manager, most of
the sediment that settles down in Cancano comes from suspended
load from the san Giacomo reservoir, because the watershed di-
rectly drained by Cancano is negligible. the val Grosina reser-
voir is periodically emptied and the mean annual sediment yield
is estimated by the observed variations of the bathymetry.
the amount of sediment settled down within these reser-
voirs is mostly representative of the fine sediment fraction: ac-
tually, the tyrolean intakes used at most of the barrages prevent
the coarse fraction of sediments from entering into the diversion
canals, where this fraction is further intercepted within settling
basins. However, EPM estimates include the full spectrum of
particle sizes and, accordingly, they are not directly comparable
with the measured data. in order to evaluate the relative impor-
tance of the volume of fine sediments with respect to the overall
sediment production estimated by EPM, a soil sampling cam-
paign, aimed at measuring the granulometric curves, was ac-
complished in nine watersheds within the investigated area (see
filled squares in Fig. 1). the sites are mostly located on acces-
sible slopes rather than in streams and they were selected in or-
der to obtain a sufficiently complete coverage of the study area.
since the studied basins are in most cases small and charac-
terized by high energy geological processes, the granulometric
distribution of sediments might be considered scarcely affected
from the sampling location and, accordingly, it was assumed
representative of the entire basin. Fig. 5 shows the averaged
granulometric curves for each group of catchments.
the percent of fine particles (Φ<0.15 mm) of each soil sam-
ple was computed using the granulometric curves. although this
percentage showed a remarkable variability, within each group of
basins the samples were consistent. the “spöl” group basins have
a mean percentage of fine materials below 5%. For the catch-
ments of the “val Grosina” group and of the “Forni” group, this
percentage is respectively 10% and 12%. Furthermore, other ag-
Fig. 5 - Averaged granulometric curves of the sampled soils
Fig. 4 - The connections between the studied groups of basins and the
related reservoirs
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
27
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
ment was measured within san Giacomo and Cancano reser-
voirs. this volume, that would correspond to an average input
of 16000 m
3
/y, is related to the fine sediment fraction from the
“Forni” and “spöl” groups and to the overall sediment yield
from the basin that is directly drained by the san Giacomo res-
ervoir. the fine sediment yield from the “Forni” and “spöl”
groups can be derived by the overall EPM computation by ap-
plying the percentages of tab. 9 and amounts to 31000 m
3
/y.
the contribution from the basin directly drained by the san Gi-
acomo reservoir increases this value up to 43500 m
3
/y. accord-
ingly, for these two groups of basin EPM provides an estimate
that is three times the measured values.
the application of EPM to the “val Grosina” group of ba-
sins provided an overall sediment yield of about 168000 m
3
/y,
of which 17400 m
3
/y are related to the fine sediment fraction.
this value, increased to 35200 m
3
/y by the sediment contribu-
gregate granulometric data (b
aSSi
, 2000) were measured for the
Cedec and Frodolfo catchments (Fig. 1), where a fine sediment
percentage of about 45% was measured.
in order to extrapolate the volume of fine sediments from
the overall EPM estimates, the percentage of fine materials was
assigned to each basin on the basis of the most representative
granulometric curve, considering geographical proximity and ge-
ological criteria based on lithological and morphological charac-
teristics of the basins. Finally, the amount of fine sediment yield
from each group was computed by multiplying the total volume
of sediment yield of each basin for the related percentage. the
basins that are directly drained by the reservoirs contribute to the
sediment yield with their whole sediment production.
a mean sediment yield of about 165000 m
3
/y was calcu-
lated by EPM for the “Forni” and “spöl” group of catchments.
after 50 years of activity, a volume of about 800000 m
3
of sedi-
Tab. 9 - Main morphological and meteorological features of the considered basins, divided in three groups. The parameters t
1
and t
2
represent the average
yearly temperature and the mean temperature of the period from May to October, both calculated at the mean altitude of the basin. h
min
and h
max
represent respectively the minimum and the maximum altitude of each basin
background image
L. MILANESI, M. PILOTTI, A. CLERICI & Z. GAVRILOVIC
28
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
mainly concentrated in the thawing period and often related to
intense rainfall events, we proposed to calculate the averaged
hydro-meteorological parameters for this temporal window
only. this modification to the original methodology allows to
remove the operational difficulties for the assessment of the
temperature coefficient in basins with negative mean annual
temperature. Both these changes widen the application scope
of the model and substitute the original classification with easy-
to-use and more clear tables, without changing the global meth-
odology. some tests on two small alpine basins showed good
agreement between the results obtained by the application of
the modified version of EPM and of the original methodology.
a simple statistical analysis was performed to compare dis-
tributed and lumped applications of EPM. the results obtained
with a set of synthetic watersheds showed maximum variations
in sediment production up to 14% between the two approaches.
accordingly, the greatest advantage of distributed approaches is
the possibility to preserve the physical meaning of the param-
eters and to represent the prevailing mechanics of soil erosion
processes. Moreover, it allows to locate easily the sediment pro-
duction areas within the catchment and to quantify their specific
contribution to the overall sediment yield.
Finally, EPM was applied to a set of 31 alpine catchments in
northern italy. in order to test the reliability of the results, they
were compared to the sedimentation data of three reservoirs
and to turbidimetric measurements. the model was applied for
the period from May to october and it was implemented using
a software specifically designed for a spatially distributed ap-
plication along the drainage network. a mean overall sediment
production of 165000 m
3
/y and 168000 m
3
/y was calculated for
the catchments drained by the san Giacomo-Cancano and val
Grosina reservoirs respectively. in order to make comparable
the calculated values with the measured siltation data (respec-
tively, 16000 m
3
/y and 17500 m
3
/y) soil sampling and granu-
lometric analysis were performed, reducing the above values
to 43500 m
3
/y and 35200 m
3
/y. Considering the complexity of
the involved processes and the high level of uncertainties (e.g.,
b
raZier
et alii, 2000), these results are in fair agreement with
the measurements and the discrepancies can be partly explained
by several considerations on reservoir management. this con-
clusion is supported by the results obtained for the Cedec and
Frodolfo catchments, where the computed values of fine sedi-
ment yield (16000 m
3
/y) are in good agreement with the inte-
tion from the directly drained basin, can be compared to about
17500 m
3
/y of sediments measured in the reservoir by bathy-
metric comparison.
in conclusion, as shown in tab. 10, in both cases EPM
overestimates the measured values of sediment yield, with
a multiplicative factor that ranges from 1.5 to 3. Considering
the range of uncertainty that affects this type of problems (e.g.,
b
raZier
et alii, 2006), the results obtained by the application
of EPM are encouraging since they are of the same order of
magnitude of the sedimentation data. a possible reason to ex-
plain the observed difference, in addition to the potential errors
deriving from the application of the model into an environment
different from the calibration one, is provided by the fact that
during flood events, when relevant sediment transport occurs,
the plants manager does not divert water to the reservoirs. this
conclusion is supported also by the measurements accomplished
at the confluence of the Frodolfo and Cedec streams (Fig. 1),
where a turbidimeter was installed since 2009, so that informa-
tion on the overall suspended load from these basins is avail-
able. this dataset provides a mean annual volume of suspended
sediments of about 18000 m
3
/y, to be compared with 16000 m
3
/y
of fine sediment yield provided by EPM for these two basins
(tab. 10). since the turbidimeter registrations are not affected
by the diversion regime, the measured mean annual volume of
suspended sediments is directly comparable to the computed
value. the match between the measured and the computed val-
ues of suspended sediment is very good and supports the reli-
ability of the overall procedure.
CONCLuSIONS
in this paper we considered some simple improvements to
stumbling blocks of the original EPM methodology, whose ap-
plication entails ambiguities and operational difficulties that are
mainly a consequence of the unclear parameters classification
tables. Moreover, when applied in areas where the annual aver-
age temperature drops below -1 °C, a second difficulty arises,
that is tied to the mathematical definition of the temperature co-
efficient (eq. 2).
in this contribution we introduced some “physically based”
changes to the classification system to increase the objectivity
and the applicability of the model, making use, among others,
of the widespread Corine Land Cover methodology. Moreo-
ver, since the most relevant erosion processes in cold areas are
Tab. 10 - Averaged results of the application of EPM to the studied basins. The Frodolfo and Cedec basin
is a subset of the “Forni” group
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APPLICATION OF AN IMPROVED VERSION OF THE EROSION POTENTIAL METHOD IN ALPINE AREAS
29
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
ACkNOwLEDGEMENTS
We wish to thank a2a staff, especially Dr. Michele De Censi,
eng. Ferdinando Bondiolotti and eng. sergio De Campo, for their
valuable suggestions and help in data collection activities. We are
also grateful to eng. stefano Barontini, precious partner in labo-
ratory activities. this work was partially developed within the eU
Project KUltUrisk FP7, Grant agreement n. 265280.
gral of the turbidimetric measurements (18000 m
3
/y). these two
volumes are directly comparable since both account for fine
sediment only and include sediment load carried during flood
events. accordingly, the link with widespread classification sys-
tems and the extension to alpine glacial and periglacial regions
makes EPM a valuable and easy-to-use instrument for soil ero-
sion mapping also in alpine areas.
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