Probabilistic landslide hazard assessment at the basin scale

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Geomorphology 72 (

Probabilistic landslide hazard assessment at the basin scale

Fausto Guzzetti *, Paola Reichenbach, Mauro Cardinali,

Mirco Galli, Francesca Ardizzone

IRPI CNR, via Madonna Alta 126, 06128 Perugia, Italy

Received 8 November 2004; received in revised form 24 May 2005; accepted 16 June 2005

Available online 15 August 2005

Abstract

We propose a probabilistic model to determine landslide hazard at the basin scale. The model predicts where landslides will

occur, how frequently they will occur, and how large they will be. We test the model in the Staffora River basin, in the northern

Apennines, Italy. For the study area, we prepare a multi-temporal inventory map through the interpretation of multiple sets of

aerial photographs taken between 1955 and 1999. We partition the basin into 2243 geo-morpho-hydrological units, and obtain

the probability of spatial occurrence of landslides by discriminant analysis of thematic variables, including morphological,

lithological, structural and land use. For each mapping unit, we obtain the landslide recurrence by dividing the total number of

landslide events inventoried in the unit by the time span of the investigated period. Assuming that landslide recurrence will

remain the same in the future, and adopting a Poisson probability model, we determine the exceedance probability of having

one or more landslides in each mapping unit, for different periods. We obtain the probability of landslide size by analysing the

frequency–area statistics of landslides, obtained from the multi-temporal inventory map. Assuming independence, we obtain a

quantitative estimate of landslide hazard for each mapping unit as the joint probability of landslide size, of landslide temporal

occurrence and of landslide spatial occurrence.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Landslides; Mathematical model; Hazard; Susceptibility; Frequency; Magnitude; GIS; Maps

1. Introduction

Landslides are important natural hazards and an

active process that contributes to erosion and landscape

evolution. Different natural phenomena and human dis-

turbances trigger landslides. Natural triggers include

0169-555X/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.geomorph.2005.06.002

* Corresponding author. Tel.: +39 075 501 4413; fax: +39 075

501 4420.

E-mail address: [email protected] (F. Guzzetti).

meteorological changes, such as intense or prolonged

rainfall or snowmelt, and rapid tectonic forcing, such as

earthquakes or volcanic eruptions. Human disturbances

include land use changes, deforestation, excavation,

changes in the slope profile, irrigation, etc. On Earth,

the volume of mass movements spans 15 orders of

magnitude, and landslide velocity extends over 14

orders of magnitude, from millimetres per year to hun-

dreds of kilometres per hour. Similarly,massmovements

can occur singularly or in groups of up to several thou-

2005) 272–299

F. Guzzetti et al. / Geomorphology 72 (2005) 272–299 273

sands. Multiple landslides, for example, occur almost

simultaneously when slopes are shaken by an earth-

quake, or over a period of hours or days when failures

are triggered by intense rainfall or snow melting. Land-

slides can involve flowing, sliding, toppling or falling

movements, and many landslides exhibit a combination

of these types of movements (Cruden and Varnes,

1996). The extraordinary breadth of the spectrum of

landslides makes it difficult to define a single metho-

dology to ascertain landslide hazard (Guzzetti, 2002).

Many methods have been proposed to evaluate

quantitatively landslide hazard geographically at the

basin scale (Carrara, 1983; Carrara et al., 1991, 1995;

van Westen, 1994; Soeters and van Westen, 1996;

Chung and Frabbri, 1999; Guzzetti et al., 1999 and

references herein). Such models are best classified as

susceptibility models (Brabb, 1984), because they pro-

vide an estimate of bwhereQ landslides are expected. Afew attempts have been made to establish the temporal

frequency of slope failures (Keaton et al., 1988; Lips

and Wieczorek, 1990; Coe et al., 2000; Crovelli, 2000;

RIVANAZZANO

Piedmont

Lombardy

Emilia-RomagnaTURIN

MILAN

BOLOGN

Fig. 1. Location of the study area

Guzzetti et al., 2002a,b). The latter models attempt to

predict bwhenQ a landslide will occur by establishing

the exceedance probability of landslide occurrence

during an established period. Most commonly, the

exceedance probability is obtained from catalogues

of historical landslide events, which are lists showing

the time (or period) of occurrence of single or multiple

slope failures. No single measure of landslide magni-

tude exists (Guzzetti, 2002). For certain landslide

types, including slides and complex failures, landslide

area is a reasonable proxy for landslide magnitude.

Recently, information has become available on the

frequency–area statistics of landslides (Hovius et al.,

1997; Stark and Hovius, 2001; Guzzetti et al., 2002a,b;

Guthrie and Evans, 2004a,b; Malamud et al., 2004).

This information can be used to determine the

expected probability of landslide area and magnitude.

In this paper, we propose a probabilistic model to

determine landslide hazards at the basin scale. The

model exploits information obtained from a multi-

temporal inventory map to predict where landslides

VARZI

M. CHIAPPA

A

N0 2 4 km1

, the Staffora River basin.

F. Guzzetti et al. / Geomorphology 72 (2005) 272–299274

will occur, how frequently they will occur, and how

large they will be. We test this model in the Staffora

River basin, in the Northern Apennines, and we dis-

cuss the results obtained.

2. The study area

The study area extends for 275 km2 in the southern

Lombardy region, in northern Italy (Fig. 1). Elevation

in the area ranges from about 150 m at Rivanazzano to

1699 m at M. Chiappa. The Staffora River, a tributary

of the Po River, drains the area. In the 42-year period

from 1951 to 1991, annual rainfall in the area ranged

from 410 to 1357 mm, with an average value of 802

mm. Precipitation is most abundant in the autumn and

in the spring (Fig. 2).

Marine, transitional and continental sedimentary

rocks, Cretaceous to Holocene in age (Servizio Geo-

logico Nazionale, 1971) outcrop in the Staffora River

basin. Marine sediments include: (i) sequences of

layered limestone, marly-limestone, marl and clay,

with ophiolites, (ii) disorganized, and highly fractured

marl and clay, overlaid by massive sandstones, and

(iii) shallow marine sediments pertaining to the Ges-

soso-Solfifera Fm. Transitional deposits feature con-

glomerates, with lenses of marl and sand, which are

Oligocene in age. Fluvial and terraced deposits, Holo-

cene in age, represent the continental deposits and

outcrop along the main valley bottoms.

The area has a complex structural setting resulting

from the superposition of two tectonic phases asso-

20

40

60

80

100

Jan

Feb

Mar

Apr

May Jun

Jul

Aug Sep

Oct

Nov

Dec

Mea

n m

onth

ly r

ainf

all (

mm

)

2

4

6

8

10

12

14

Perc

enta

ge o

f m

ean

annu

al r

ainf

all (

%)

Fig. 2. Monthly rainfall values (left y-axis) and percentages (right y-

axis) for the period between 1951 and 1990 for the Varzi rain gauge,

416 m a.s.l.

ciated to the formation of the Apennines mountain

chain. A compressive phase of Cretaceous to Eocene

age produced large, north–east verging thrusts with

associated anticlines, synclines and transcurrent faults,

and was followed by an extensional tectonic phase of

Oligocene to Holocene age, which produced chiefly

normal faults. The lithological and the structural set-

tings control the morphology of the area, which fea-

tures steep and asymmetric slopes, dissected by a

dense, locally actively eroding stream network. Land-

slides are abundant in the area, and range in type and

size from large rotational and translational slides to

deep and shallow flows. Some of the landslides are

presumably very old in age. Very old landslides are

mostly relict or dormant, and are partially concealed

by forest and the intensive farming activity.

3. Mathematical model

Varnes and the IAEG Commission on Landslides

and other Mass-Movements (1984) proposed that the

definition adopted by the United Nations Disaster

Relief Organization (UNDRO) for all natural hazards

be applied to the hazard posed by mass movements.

Varnes and his co-workers defined the landslide

hazard as bthe probability of occurrence within a

specified period of time and within a given area of a

potentially damaging phenomenonQ. Guzzetti et al.

(1999) amended the definition to include the magni-

tude of the event. In contrast to other natural hazards,

no unique measure of landslide magnitude is available

(Hungr, 1997). For earthquakes, magnitude is a mea-

sure of the energy released during an event. For land-

slides, a measure of the energy released during failure

is difficult to obtain. Hungr (1997) proposed destruc-

tiveness to be a measure of landslide magnitude.

Cardinali et al. (2002b) and Reichenbach et al.

(2005) defined landslide destructiveness as a function

of the landslide volume and of the expected landslide

velocity, the latter obtained from the landslide type.

For large areas, landslide volume and velocity are

difficult to evaluate systematically, making the

approach impracticable. Alternatively, where slope

failures are chiefly slow-moving slides and slide

earth-flows, destructiveness can be related to the

area of the landslide, information that is readily avail-

able from accurate landslide inventory maps.


The definition of landslide hazard incorporates the

concepts of location, time and size. To complete a

hazard assessment one has to predict (quantitatively)

bwhereQ a landslide will occur, bwhenQ or how fre-

quently it will occur, and bhow largeQ the landslide

will be. In mathematical terms, this can be written as:

HL ¼ P½ALzaLin a time interval t; given

fmorphology; lithology; structure; landuse; . . . g�ð1Þ

where, AL is the area of a landslide greater or equal

than a minimum size, aL, measured, for example, in

square meters. For any given area, Eq. (1) expresses

landslide hazard as the conditional probability of land-

slide size, PAL, of landslide occurrence in an estab-

lished period t, PN, and of landslide spatial

occurrence, S, given the local environmental setting.

Assuming independence among the three probabil-

ities, the landslide hazard, i.e. the joint probability is:

HL ¼ PAL� PN � S ð2Þ

From a geomorphological point of view, the

assumption that the three probabilities (i.e., the three

components of landslide hazard) are independent is

strong and may not hold always and everywhere. In

many areas we expect slope failures to be more fre-

quent (time component) where landslides are more

abundant and landslide area is large (spatial compo-

nent). However, given the lack of understanding of the

landslide phenomena, independence is an acceptable

first-approximation that makes the problem mathema-

tically tractable and easier to work with.

3.1. Probability of landslide size

The probability that a landslide will have an area

greater or equal than aL is:

PAL¼ P ALzaL½ � ð3Þ

and can be estimated from the analysis of the fre-

quency–area distribution of known landslides,

obtained from landslide inventory maps. Analysis of

accurate landslide inventories reveals that the abun-

dance of landslides increases with landslide area up to

a maximum value, where landslides are most frequent,

then it decays rapidly along a power law (Pelletier et

al., 1997; Hovius et al., 1997; Stark and Hovius, 2001;

Guzzetti et al., 2002a,b; Guthrie and Evans, 2004a,b;

Malamud et al., 2004).

Malamud et al. (2004) analysed three recent and

well documented landslide inventories from California

(Harp and Jibson, 1996), central Italy (Cardinali et al.,

2000; Guzzetti et al., 2002a,b) and Guatemala (Buck-

nam et al., 2001), and found the probability density

function (PDF) of landslide area, AL, to be in good

agreement with a truncated inverse gamma distribu-

tion. These authors proposed that the PDF of landslide

area can be estimated as (Malamud et al., 2004):

p AL; q; a; sð Þ ¼ 1

aC qð Þa

AL s

� �qþ1

exp a

AL s

� �ð4Þ

where: C(q) is the gamma function of q, and q N0,

aN0, and sVALbl are parameters of the distribution.

In Eq. (4), q controls the power–law decay for medium

and large landslide areas, a primarily controls the

location of the maximum of the probability distribu-

tion, and s primarily controls the exponential decay for

small landslide areas. Fitting Eq. (4) to the three avail-

able inventories, Malamud et al. (2004) found

q =1.40, a =1.28d 103 m2, and s=1.32d 102 m2

(determination coefficient r2=0.965).

Using Eq. (4), PALis given by:

PAL¼Z l

aL

p AL; q; a; sð ÞdAL ¼Z l

aL

1

aC qð Þa

AL s

� �qþ1

� exp a

AL s

� �dAL ð5Þ

In another study of frequency–area statistics of

landslides, Stark and Hovius (2001) analyzed three

landslide datasets obtained from New Zealand and

Taiwan and found the PDF of landslide area to be in

good agreement with a double Pareto probability dis-

tribution. Using this distribution, PALis given by (Stark

and Hovius, 2001):

PAL¼

Z l

aL

p AL; a; b; l;m; cð ÞdAL

¼Z l

aL

bl 1 dð Þ

1þ m=lð Þa½ �b=a

1þ AL=lð Þa½ �1þ b=að Þ

" #

� AL=lð Þ aþ1ð ÞdAL ð6Þ

where: a N0, b N0, 0VcV lVmVl, and with


d ¼ y cð Þ ¼ 1þ m=lð Þa

1þ AL=lð Þa

h ib=a. Note that a in Eq. (6) is the

same as q in Eqs. (4) and (5) and controls the power-

law decay of landslide probability for large landslide

areas. Also, b in Eq. (6) controls the power-law

decays for small landslide areas.

Use of Eqs. (4)–(6) requires the catalogue of land-

slide areas from which the distributions are derived to

be statistically substantially complete, i.e. that most of

the landslides that have occurred in the region were

mapped accurately (Malamud et al., 2004).

3.2. Temporal probability of landslides

As a first approximation, landslides can be consid-

ered as independent random point-events in time

(Crovelli, 2000). In this framework, the exceedance

probability of occurrence of landslide events during

time t is:

PN ¼ P N tð Þz1½ � ð7Þ

where N(t) is the number of landslides that occur

during time t in the investigated area.

Two probability models are commonly used to

investigate the occurrence of naturally occurring ran-

dom point-events in time: the Poisson model and the

binomial model (Crovelli, 2000; Onoz and Bayazit,

2001). The Poisson model is a continuous-time model

consisting of random-point events that occur indepen-

dently in ordinary time, which is considered naturally

continuous. The Poisson model has been used to

investigate the temporal occurrence of, for example,

volcanic eruptions (Klein, 1982; Connor and Hill,

1995; Nathenson, 2001), floods (e.g. Yevjevich,

1972; Onoz and Bayazit, 2001), and landslides (e.g.

Crovelli, 2000; Coe et al., 2000). Adopting a Poisson

model for the temporal occurrence of landslides, the

probability of experiencing n landslides during time t

is given by (Crovelli, 2000):

P N tð Þ ¼ n½ � ¼ exp ktð Þ ktð Þn

n!n ¼ 0; 1; 2; . . .

ð8Þ

where k is the estimated average rate of occurrence of

landslides, which corresponds to 1 /l, with l the

estimated mean recurrence interval between succes-

sive failure events. The variables k and l can be

obtained from a historical catalogue of landslide

events, or from a multi-temporal landslide inventory

map.

From Eq. (8), the probability of experiencing one

or more landslides during time t (i.e. the exceedance

probability) is:

P N tð Þz1½ � ¼ 1 P N tð Þ ¼ 0½ � ¼ 1 exp ktð Þ¼ 1 exp t=lð Þ ð9Þ

Discussing Eq. (9), Crovelli (2000) notes that for a

given period of time t, if lYl, then P[N(t)z1]Y0,

i.e. if the estimated mean recurrence interval between

successive events is very large, chances are that no

slope failures will be experienced in the considered

period. Also, if the estimated mean recurrence l is

fixed, and the time interval is very long (tYl), then

P[N(t)z1]Y1, and one is certain to observe a land-

slide event.

The Poisson model allows for determining the

probability of future landslides for different times t

(i.e. for different numbers of years) based on the

statistics of past landslide events, under the following

assumptions (Crovelli, 2000): (i) the number of land-

slide events that occur in disjoint time intervals are

independent; (ii) the probability of an event occurring

in a very short time is proportional to the length of

the time interval; (iii) the probability of more than

one event in a short time interval is negligible; (iv)

the probability distribution of the number of events is

the same for all time intervals of fixed length; and (v)

the mean recurrence of events will remain the same

in the future as it was observed in the past. The

consequences of these assumptions, which may not

always hold for landslide events, should be consid-

ered when interpreting (and using) the results of the

probability model.

As an alternative to the Poisson model, a binomial

model can be adopted. The binomial probability

model is a discrete-time model consisting of the

occurrence of random-point events in time. In this

model, time is divided into discrete increments of

equal length. Within each time increment a single

point-event may or may not occur. The binomial

model was adopted by Costa and Baker (1981) to

investigate the occurrence of floods, and by Keaton

et al. (1988), Lips and Wieczorek (1990), and Coe et

al. (2000) to study the temporal occurrence of land-

slides and debris flows.


Following Crovelli (2000), and adopting the bino-

mial probability model, the exceedance probability of

experiencing one or more landslides during time t is:

P N tð Þz1½ � ¼ 1 P N tð Þ ¼ 0½ � ¼ 1 1 pð Þt

¼ 1 1 1=lð Þt ð10Þ

where, p is the estimated probability of a landslide

event in time t, and l =1 /p is the estimated mean

recurrence interval between successive slope failures.

As for the Poisson model, l can be obtained from a

historical catalogue of landslides or from a multi-

temporal landslide inventory map. The binomial prob-

ability model holds under the same or similar assump-

tions listed for the Poisson model.

Crovelli (2000) compared the Poisson and the

binomial probability models, and showed that the

two models differ for short mean recurrence intervals

(i.e. when l is small) and for short periods (i.e. when t

is small), with the binomial model over-estimating the

exceedance probability of future landslide events. For

long periods and large mean recurrence intervals, i.e.,

for rare events, the bimodal model coincides with the

Poisson model.

3.3. Spatial probability of landslides

The spatial probability of landslide occurrence,

also known as susceptibility (Brabb, 1984), is the

probability that any given region will be affected by

landslides, given a set of environmental conditions.

Defining:

L : a given region will be affected by landslides

ð11Þ

susceptibility, S, becomes:

S ¼ P L is true; given½fmorphology; lithology; structure; landuse; etc:g�

ð12Þ

or,

S ¼ P Ljv1 rð Þ; v2 rð Þ; . . . ; vm rð Þ½ � ð13Þ

which is the joint conditional probability that a region

r will be affected by future landslides given the m

environmental variables v1, v2, . . ., vm in the same

region.

Susceptibility can be estimated using a variety of

statistical techniques, which include among others

discriminant analysis (Reger, 1979; Carrara, 1983;

Carrara et al., 1991, 1992, 1995, 2003; Guzzetti et

al., 1999; Nagarajan et al., 2000; Baeza and Coro-

minas, 2001; Ardizzone et al., 2002; Cardinali et al.,

2002a; Santacana et al., 2003), logistic regression

analysis (Carrara et al., 1992; Atckinson and Mas-

sari, 1998; Rowbotham and Dudycha, 1998; Dai and

Lee, 2002, 2003; Olhmacher and Davis, 2003; Lee,

2004; Suzen and Doyuran, 2004; Ayalew and Yama-

gishi, 2005), and conditional analysis based on a

variety of favourability functions like weight of evi-

dence (Bonham-Carter, 1991; Lee et al., 2002a,b;

Wu et al., 2004), weighting factors (Cevik and

Topal, 2003), weighted linear combination of

instability factors (Ayalew et al., 2004), likelihood

ratio (Chung and Fabbri, 2003, 2005; Fabbri et al.,

2003; Lee, 2004), certainty factors (Binaghi et al.,

1998), information value (Lin and Tung, 2004), and

modified Bayesian estimation (Chung and Frabbri,

1999).

Depending on the type of statistical technique, the

meaning of the probability changes slightly. When

using discriminant analysis or logistic regression

analysis, the probability assigned to any given area

(i.e. to each terrain or mapping unit) is the prob-

ability that the area pertains to one of two groups,

namely: (i) the group of mapping units having land-

slides, P1, or (ii) the group of mapping units free of

landslides, P0, given the set of environmental con-

ditions used in the analysis. At the beginning of a

study only past landslides in a region are known.

Hence, classification of landslide-bearing and land-

slide-free mapping units is made based on the known

distribution of past slope failures. A straightforward

deduction is to assume S =P[raP1]=1P[raP0].

In other words, if a region r pertains to the group of

mapping units having known (i.e. past) landslides

(e.g. P1) because of the local environmental condi-

tions, it is likely that the same region will experience

slope failures again in the future (even if we do not

know when). Equally, if a region pertains to the

group of mapping units free of (known) landslides

(e.g. P0) it is unlikely that the same region will

experience mass movements.

Chung and Frabbri (1999) proposed to estimate

the probability of future landslides in any given


region, S, from the probability of past landslides in

the same region, given a set of environmental vari-

ables. Letting:

F : a given region has been affected by landslides;

ð14Þ

the joint conditional probability of past landslides in

a region r, given the m environmental variables v1,

v2, . . ., vm in the same region is:

D ¼ P Fjv1 rð Þ; v2 rð Þ; . . . ; vm rð Þ½ � ð15Þ

From Eqs. (13) and (15) it follows that:

P Ljv1 rð Þ; v2 rð Þ; . . . ; vm rð Þ½ � ¼ P Fjv1 rð Þ;½v2 rð Þ; . . . ; vm rð Þ�; ð16Þ

or S =D. To estimate the spatial probability of past

landslides (and infer from it the spatial probability

of future failures), the study area is partitioned into

unique condition units (UCU), i.e. areas character-

ized by an exclusive (unique) combination of envir-

onmental conditions. This can be easily obtained in

a GIS by the geographical union of all thematic

layers available for the study area. The spatial

probability of past landslide occurrence is then sim-

ply estimated from the density of landslides in each

UCU.

Chung and Frabbri (1999) showed that D is a

good descriptor of the past (known) landslides,

conditioned to the available environmental informa-

tion, but it may not be a good estimator of the

future spatial occurrence of landslides, S. They

proposed more efficient indexes to estimate the

future occurrence of landslides from the observed

past distribution of slope failures, including: (i) a

Bayesian estimation under the condition of indepen-

dence, (ii) a regression model based on bivariate

conditional probabilities, (iii) a modified Bayesian

estimator under the condition of independence, and

(iv) a modified regression model based on bivariate

conditional probabilities. The two modified models

incorporate expert knowledge, i.e. information

which is not included in the original landslide or

thematic data, and that is used to modify the

observed frequency of occurrence of landslides to

fit the expert’s understanding of landslide phenom-

ena (Chung and Frabbri, 1999). This is an improve-

ment over other modelling approaches, particularly

where information on past landslides is limited or

imprecise.

Quantitative susceptibility models can predict the

spatial occurrence of future landslides under the gen-

eral assumption that in any given area slope failures

will occur in the future under the same circumstances

and because of the same conditions that caused them

in the past. This is a geomorphological rephrase of

bthe past is the key to the futureQ, which is a direct

consequence of the well-known principle of unifor-

mitarianism. However, the principle may not hold for

landslides. New, first-time failures occur under con-

ditions of peak resistance (friction and cohesion),

whereas reactivations occur under intermediate or

residual conditions. It is well known that terrain

gradient is an important factor for the occurrence of

landslides. An obvious effect of a slope failure is to

change the morphology of the terrain where the fail-

ure occurs. In addition, when a landslide moves it

may change the hydrological conditions of the slope.

It is also well known that landslides can change their

type of movement and velocity with time. Lastly,

landslide occurrence and abundance are a function

of environmental conditions that vary with time at

different rates. Some of the environmental variables

are affected by human actions (e.g. land use, defor-

estation, irrigation, etc.), which are also highly

changeable. Because of these complications, each

landslide occurs in a distinct environmental context,

which may have been different in the past and that

might be different in the future. Despite these limita-

tions, in this work we assume that the principle of

uniformity hold bstatisticallyQ, i.e. that in the investi-

gated region future landslides will occur on average

under the same circumstances and because of the

same conditions that triggered them in the past. We

further assume that our knowledge of the distribution

of past failures is reasonably accurate and complete.

We accept these simplifications to make the problem

tractable.

4. Landslide hazard assessment

To ascertain landslide hazard we partitioned the

Staffora basin into mapping units (Guzzetti et al.,


1999), adopting the procedure proposed by Carrara

et al. (1991). Starting from a digital terrain model

with a ground resolution of 20 m�20 m and a

simplified representation of the main drainage lines,

specialized software (Carrara et al., 1991; Detti and

Pasqui, 1995) was used to partition the territory

into individual slope units, bounded by drainage

and divide lines. For each slope unit, the software

computed 21 morphometric and hydrological para-

meters useful in explaining the spatial distribution

of landslides (Carrara et al., 1991, 1995). We

further subdivided the slope units according to the

main rock types cropping out in the basin. In this

way, we partitioned the study area into 2243 map-

ping units based on lithology, morphology and

hydrology (geo-morpho-hydrological terrain units),

which represent the mapping units used for the

hazard assessment.

4.1. Landslide identification and mapping

We obtained information on the geographical and

temporal distribution of landslides and on landslide

size from a detailed multi-temporal inventory map,

prepared through the interpretation of multiple sets

of aerial photographs. For the study area, five sets of

aerial photographs were available to us (Table 1). We

used each set of aerial photographs separately to

obtain different landslide inventory maps (Fig. 3).

We then merged in a GIS the five individual land-

slide maps to obtain the multi-temporal inventory

map (Fig. 3F).

Table 1

Staffora River basin

Code Flight Date Type Nominal scale

A GAI-IGMI 18 July

1955

Black and

white

1 :33,000

B ALI FOTO Winter

1975

Black and

white

1 :15,000

C TEM 1 Summer

1980

Colour 1 :22,000

D Lombardy Summer

1994

Black and

white

1 :25,000

E IT 2000 22 June

1999

Colour 1 :40,000

Aerial photographs used to compile the multi-temporal landslide

inventory map.

A team of three geomorphologists carried out inter-

pretation of the aerial photographs in a period of 6

months. Two team members looked at each pair of

aerial photographs using a mirror stereoscope (with a

magnification of 4�) that allowed both interpreters to

map contemporaneously on the same stereo pair. The

third photo-interpreter independently reviewed, and

where necessary corrected the interpretations of the

other two, using a high magnification (up to 20�)

stereoscope. For the interpretation, we used all geolo-

gical and geomorphological information available to

us from published maps, previous works carried out in

the same area, and discussion with other geologists

(Rossetti, 1997; Antonini et al., 2000; Ardizzone et

al., 2002).

Landslide information collected through the inter-

pretation of aerial photographs was visually trans-

ferred to topographic maps at 1 :10,000 scale. We

transferred geomorphological information from the

base maps onto stable, transparent sheets and scanned

these to obtain black and white, raster images of each

map sheet. We used a scanning resolution of 300–400

dpi, which corresponded to a ground resolution of less

than 0.1 m. The raster representation of the geomor-

phological line images was changed in a GIS into

vector format using a semi-automatic procedure,

which allowed us to assign attributes to each line

segment. Polygons were then constructed and labelled

with the appropriate codes, depending on their land-

slide properties.

In the separate inventory maps (Fig. 3A–E), we

classified landslides according to the type of move-

ment, and the estimated age, activity, depth, and

velocity. We defined landslide type according to

Cruden and Varnes (1996), and the WP/WLI

(1990). For deep-seated slope failures, we mapped

separately the landslide crown (depletion area) from

the deposit. Landslide age, activity, depth, and

velocity were determined based on the type of

movement, the morphological characteristics and

appearance of the landslide on the aerial photo-

graphs, the local lithological and structural setting,

and the date of the aerial photographs. We categor-

ized landslide age as recent, old or very old,

despite ambiguity in the definition of the age of a

mass movement based on its appearance (Wiec-

zorek, 1984). Landslides were classified active

(WP/WLI, 1993) where they appeared fresh on

Fig. 3. Landslide inventory maps for the Staffora River basin. Capital letters indicate the year of the aerial photographs used to compile the

inventory. See Table 2 for reference. Map F shows the entire multi-temporal inventory, which includes relict and old slides (shown in grey)

identified in the 1955 aerial photographs not shown in the other maps.



the aerial photographs (of a given date). Mass move-

ments were classified as deep-seated or shallow,

depending on the type of movement and the estimated

landslide volume. The latter was based on the type of

failure, and the morphology and geometry of the

detachment area and the deposition zone. Landslide

velocity (WP/WLI, 1995; Cruden and Varnes, 1996)

was considered a proxy of landslide type, and classi-

fied accordingly. We acknowledge that the adopted

classification scheme suffers from simplifications and

required geomorphological deduction, but it fits the

available information on landslide types and process in

the northern Apennines (Rossetti, 1997).

Table 2 shows the number, total extent and area

statistics of the landslides identified in the five sets

of aerial photographs. We identified the largest num-

ber of failures and the largest landslide area in the

1955 photographs, which show landslide of much

older age. In the other flights, we identified only new

and recent landslides. The entire landslide inventory

shows 3922 landslides, including 89 very old, relict

mass movements. The multi-temporal map covering

an undefined period from pre-1955 to 1999 (A1–E2

in Table 2) shows 3833 landslides, and does not

include the relict landslides. The multi-temporal

inventory map covering the 45-year period from

1955 to 1999 (A2–E2 in Table 2) shows 2390 land-

Table 2


Inventory Estimated landslide age Landslide

Number # Density #/km

A0 Very old (relict) 89 0.32

A1 Older than 1955 1443 5.27

A2 1955 active 306 1.12

B1 1955–1975 318 1.16

B2 1975 active 685 2.50

C1 1975–1980 89 0.32

C2 1980 active 305 1.11

D1 1980–1994 455 1.66

D2 1994 active 175 0.63

E1 1994–1999 19 0.07

E2 1999 active 38 0.14

A0–A1 Very old to older than 1955 1532 5.57

A0–E2 Very old to 1999 active 3922 14.26

A1–E2 Older than 1955 to 1999 active 3833 13.93

A2–E2 1955 active to 1999 active 2390 8.69

Landslide size and abundance. For dates of aerial photographs see Table

* The percentage of landslide area is computed with respect to the total

slides. Table 3 lists the landslide types identified in

the individual maps and shown in the multi-temporal

inventory map.

4.2. Probability of landslide size

To ascertain the probability of landslide area, we

selected the multi-temporal inventory map covering

the 45-year period from 1955 to 1999 (2390 land-

slides, A2–E2 in Table 2). We obtained the area of

each landslide from the GIS. Care was taken to

calculate the exact size of each landslide, avoiding

topological and graphical problems related to the

presence of smaller landslides inside larger mass

movements. For convenience, we merged the

crown area and the deposit, and we used the total

landslide area in the analysis. We used only recent

and active landslides, and we excluded the old and

relict mass movements.

Fig. 4A shows the probability density function

(PDF) of landslide areas in the Staffora basin. Two

estimates of the PDF are shown. We obtained the first

estimate using the truncated inverse-gamma function

of Malamud et al. (2004) (Eq. (4)). For this estimate,

97.5% confidence intervals are also shown. We

obtained the second estimate using the double-Pareto

function of Stark and Hovius (2001) (Eq. (6)). In the

Landslide area

2 Total km2 Percentage* % Min m2 Mean m2 Max m2

34.72 49.30 57,300 390,100 2,384,900

38.24 54.30 900 27,900 826,700

2.46 3.49 700 8000 163,400

2.38 3.39 200 7500 51,000

4.41 6.26 100 6500 114,700

1.32 1.87 400 14,800 119,100

2.40 3.41 500 7900 119,100

2.06 2.92 500 4500 177,800

1.36 1.94 500 7800 77,900

0.65 0.93 3600 34,300 119,100

0.85 1.21 1900 22,400 119,100

63.22 90 900 41,300 2,384,900

70.42 100 100 17,900 2,384,900

46.43 66 100 12,100 177,800

12.08 17 100 3600 177,800

1.

area covered by landslides (A0–E2).

Table 3


Inventory Estimated landslide age Landslide types

I II III IV V VI VII ALL

A0 Very old (relict) 0 0 0 0 0 41 48 89

0% 0% 0% 0% 0% 8.3% 6.0% 2.2%

A1 Older than 1955 121 7 15 253 55 357 635 1443

10.5% 3.6% 62.5% 25.7% 20.0% 72.8% 78.9% 36.8%

A2 1955 active 149 26 2 86 26 7 10 306

13.0% 13.3% 8.3% 8.7% 9.6% 1.4% 1.2% 7.8%

B1 1955–1975 60 4 0 93 52 30 79 318

5.2% 2.1% 0.0% 9.5% 18.9% 6.2% 9.8% 8.1%

B2 1975 active 291 32 3 254 60 29 16 685

25.3% 16.4% 12.5% 25.8% 21.8% 5.9% 2.0% 17.5%

C1 1975–1980 23 15 0 26 20 4 1 89

2.0% 7.7% 0.0% 2.6% 7.3% 0.8% 0.1% 2.3%

C2 1980 active 71 33 0 132 48 12 9 305

6.2% 16.9% 0.0% 13.4% 17.3% 2.4% 1.1% 7.8%

D1 1980–1994 293 29 0 121 5 5 2 455

25.5% 14.9% 0.0% 12.4% 1.8% 1.1% 0.2% 11.6%

D2 1994 active 132 23 4 5 2 5 4 175

11.5% 11.8% 16.7% 0.5% 0.7% 1.1% 0.6% 4.5%

E1 1994–1999 2 10 0 5 1 0 1 19

0.2% 5.1% 0.0% 0.5% 0.4% 0.0% 0.1% 0.5%

E2 1999 active 7 16 0 9 6 0 0 38

0.6% 8.2% 0.0% 0.9% 2.2% 0.0% 0.0% 1.0%

A0–A1 Very old to

older than 1955

121 7 15 253 55 398 683 1532

10.5% 3.6% 62.5% 25.7% 20% 81.2% 84.8% 39.0%

A0–E2 Very old to

1999 active

1149 195 24 984 275 490 805 3922

100% 100% 100% 100% 100% 100% 100% 100%

A1–E2 Older than 1955

to 1999 active

1149 195 24 984 275 449 757 3833

100% 100% 100% 100% 100% 91.6% 94.0 97.7%

A2–E2 1955 active to

1999 active

1028 188 9 731 220 92 122 2390

89.5% 96.4% 37.5% 74.3% 80% 18.8% 15.2% 61.0%

Number (normal text) and percentage (italic) of landslide types.

(I) single flows; (II) multiple small flows; (III) deep-seated flows; (IV) shallow slides; (V) shallow slide-earth flows; (VI) deep-seated slide-earth

flows; (VII) deep-seated slides; (ALL) all landslide types.


study area the two functions provide very similar

results, and differ slightly in the slope of the tail of

the distribution (for inverse gamma, q +1=2.77, std.

dev.=0.08, for double Pareto, a +1=2.50, std.

dev.=0.05). Fig. 4B shows the probability of landslide

size, i.e. the probability that a landslide will have an

area smaller than a given size (left axis), or the prob-

ability that a landslide will have an area that exceeds a

given size (right axis). Fig. 4B also shows the prob-

ability that a landslide in the Staffora River basin

exceeds an area of 2000 m2 and an area of 10,000

m2 (1 ha), which are found 0.75 and 0.15, respec-

tively. We will use these values to ascertain the land-

slide hazard.

4.3. Frequency of occurrence of landslides

The proposed model for landslide hazard requires

an estimate of the temporal probability of slope

failures. The availability of a multi-temporal land-

slide inventory map (Fig. 3) allowed us to estimate

the frequency of landslide occurrence in each map-

ping unit. To obtain an estimate of the frequency of

landslide occurrence, we first counted the number of

landslides in each mapping unit. Considering only

the new or reactivated landslides (A2–E2 in Table 2),

we prepared a map of the total number of landslide

events (occurrences) in the 45-year period between

1955 and 1999, the dates of the oldest and the most

Landslide Area, AL (m2)

Prob

abili

ty d

ensi

ty, p

(m

-2)

Double Pareto

Inverse Gamma

Landslide Area, AL (m2)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Prob

abili

ty, P

[AL <

L]

Double Pareto

Inverse Gamma

102 103 104 105 106

100 1,000 10,000 100,000 1,000,0001.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Prob

abili

ty, P

[AL ≥

L]

10,000 m2

2000 m2

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-9

10-8

10-7

10-6

10-5

10-4

10-3

1100 1,000 10,000 100,000 1,000,000

102 103 104 105 106

A

B

a a

Fig. 4. Probability density (A) and probability (B) of landslide area in the Staffora River basin. Solid black line is a truncated inverse gamma

function (Malamud et al., 2004). Dotted line is a double Pareto function (Stark and Hovius, 2001). Error bars show 97.5% confidence

intervals.


recent aerial photographs. For each mapping unit,

based on the past rate of landslide occurrence we

obtained landslide recurrence, i.e. the expected time

between successive failures. Knowing the mean

recurrence interval of landslides in each mapping

unit (from 1955 to 1999), assuming the rate of

slope failures will remain the same for the future,

and adopting a Poisson probability model (Eq. (9)),

we computed the exceedance probability of having

one or more landslides in each mapping unit. Fig. 5

Fig. 5. Exceedance probability of landslide occurrence obtained computing the mean recurrence interval of past landslide events from the multi-

temporal inventory (Fig. 3), assuming it will remain the same for the future, and adopting a Poisson probability model (Eq. (9)). Shades of grey

show exceedance probability for different periods: A) 5 years, B) 10 years, C) 25 years, D) 50 years. Square bracket indicates class limit is

included; round bracket indicates class limit is not included.


(A–D) shows the exceedance probability for different

periods, from 5 to 50 years. Similar maps can be

prepared for any period. As expected, the probability

of having one or more slope failures increases with

time. Based on the historical record of landslides

obtained from the multi-temporal inventory map,

after 50 years most of the slopes in the basin have a

medium to high probability of experiencing mass

A

0

5

10

15

20

25

30

35

1850

1860

1870

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

0

50

100

150

200

250

300

350

400

Num

ber

of la

ndsl

ides

Cum

ulat

ive

num

ber

of la

ndsl

ides

B

C

Recurrence from Inventory

Rec

urre

nce

from

Cat

alog

ue

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

N0 2 4 km 1


movements. We will use the obtained estimates to

ascertain landslide hazard.

For the Staffora River basin, an historical catalogue

of damaging landslides is available (Regione Lombar-

dia, 2002). The catalogue was compiled through the

systematic screening of newspapers and local

archives, and covers the period from 1850 to 1997,

listing 389 slope failures at 243 sites (Fig. 6A). A

comparison between the expected time between fail-

ures obtained from the multi-temporal inventory map,

and the information listed in the historical catalogue is

not straightforward. Most of the information listed in

the historical catalogue refers to landslides that caused

damage in urban areas or along the road network.

With this respect, the historical catalogue is less sys-

tematic than the mapping obtained through the inter-

pretation of aerial photographs, which provides a

more comprehensive view of the occurrence of land-

slide events in the basin. The historical catalogue

covers a longer period of time (148 years) than the

multi-temporal inventory (45 years). However, com-

pleteness of the historical catalogue varies with time.

Lack of historical landslide events before 1950 (Fig.

6B) is due to incompleteness in the catalogue, and to

the lesser number of vulnerable elements (e.g. roads,

houses) in the study area in the early period of the

catalogue.

We attempted a quantitative comparison between

the two sources of information on past landslides. For

each mapping unit, we selected the events listed in the

historical catalogue that occurred during or after 1950,

and we computed the mean recurrence of failures. We

then compared the result with the mean recurrence of

landslides obtained from the multi-temporal inventory

map (Fig. 6C). On average, mean recurrence is larger

for the multi-temporal inventory, indicating a more

systematic mapping. Inspection of Fig. 6C reveals that

a few mapping units exhibit greater recurrence for the

historical catalogue than for the multi-temporal inven-

Fig. 6. Historical landslide events in the Staffora River basin in the

period between 1850 and 1997. A) Map showing the location of 243

sites affected by 389 damaging slope failures in the considered

period. B) Annual number (histogram) and cumulative numbe

(line) of landslide events in the considered period. C) Comparison

between landslide recurrence obtained from the multi-tempora

inventory (x-axis) and the historical catalogue of landslide events

( y-axis).

r

l


tory map. Most of the slope failures listed in the

historical catalogue and located in these mapping

units (60%) occurred from 1956 to 1974, a period

for which aerial photographs were not available. Spe-

cific triggers (e.g., in 1959, 1960 and 1985) produced

many historical damaging landslides. For these trig-

gers, aerial photographs were also not available. In

addition, damaging slope failures in these mapping

units were small or very small, making their recogni-

tion on the aerial photographs very difficult.

4.4. Landslide susceptibility

The model for landslide hazard involves a quanti-

tative estimate of the probability of spatial landslide

occurrence, i.e. of susceptibility. We obtained land-

slide susceptibility through discriminant analysis of

46 thematic variables, including morphology (24 vari-

ables derived from a 20 m�20 m DTM), lithology

(14 variables), structure (3 variables) and land use (5

variables). Using GIS technology, we computed the

percentage of the individual thematic variables in each

mapping unit. The obtained values were the indepen-

dent variables in the statistical analysis. We then

computed the percentage of landslide area in each

mapping unit. Very old landslides (A0 in Table 2)

were excluded from the landslide inventory, and con-

sidered as a thematic variable, i.e., as an additional

independent variable describing the strength of the

lithological types. Following the procedure adopted

by Carrara et al. (1991), we selected a threshold of 3%

of landslide area to establish if a mapping unit was: (i)

free of landslides (V3%), or (ii) contained slope fail-

ures (N3%). We selected the threshold to account for

possible mapping, drafting and digitizing errors in the

compilation of the landslide inventory map (Carrara et

al., 1991).

Fig. 7 shows the results of five statistical models

prepared using the same set of environmental vari-

ables, and changing incrementally the landslide inven-

tory map. We prepared the first susceptibility model

Fig. 7. Landslide susceptibility models obtained through discriminate anal

changing the landslide inventory map (dependent variable, Fig. 3 and Table

using landslides in the period A1–B2; C) using landslides in the period A1

the period A1–E2. Shades of gray indicate spatial probability, in 5 class

indicates class limit is not included.

(Fig. 7A) using only landslides identified in the 1955

photographs (Fig. 3A). These landslides included

recent (in 1955) and old landslides that were visible

in the aerial photographs used to compile the inven-

tory, but not the very old and relict landslides present

in the study area (A1–A2 in Table 2). We then added to

the inventory map the new landslides identified in the

1975 aerial photographs (Fig. 3B) and we obtained a

new estimate of the probability of spatial landslide

occurrence (Fig. 7B). We repeated the same procedure

adding the slope failures that we identified and

mapped using the 1980, 1994, and 1999 aerial photo-

graphs (Fig. 3C–E). Results are shown in Fig. 7C, D

and E, respectively. At each step, we obtained a

different susceptibility map, i.e. a different estimate

of the probability of spatial landslide occurrence.

Table 4 lists the variables entered into the five dis-

criminant models. In Table 4, the standard discrimi-

nant function coefficients (SDFC) show the relative

importance of each variable in the discriminant func-

tion as a predictor of slope instability. Variables with

large coefficients (in absolute value) are strongly

associated with the presence/absence of landslides.

The sign of the coefficient tells if the variable is

positively or negatively correlated to the stability of

the mapping unit.

Twenty-six of the 46 thematic variables (58%)

entered in all five susceptibility models, confirming

their importance in explaining the geographical distri-

bution of past landslides. Variables entered in all five

models include (Table 4) morphological (ORDER,

LINK_LEN, SLO_AREA, R, SLO_ANG, SLO_

ANG2, ANG_STD, LNK_ANG, CONV, COC_COV,

RET, CC, TR1), lithological (ALLUVIO, AR_

BIS, AR_R_M_P, DETRITO, MR_AN_LO, MR_

B_R_C, MR_BOSM, MR_P_R_B), and land use

(BD, BMD, INC, PRA, SEM, REG) parameters, and

the presence of very old, relict landslide deposits

(FRA_OLD). Inspection of Table 4 reveals that 8

thematic variables entered all five models with

large standard discriminant function coefficients

ysis of the same set of independent thematic variables (Table 4) and

2). A) Using landslides identified in the period A1–A2 (Table 2); B)

–C2; D) using landslides in the period A1–D2; E) using landslides in

es. Square bracket indicates class limit is included; round bracket



(SDFCN |0.200|), equally distributed between nega-

tive (unstable) and positive (stable) values, including

the slope-unit hydrological order (ORDER), the

slope-unit gradient (SLO_ANG, SLO_ANG2), the

slope of the drainage channel (LNK_ANG), the topo-

graphic profile of the slope-unit (CC), the presence of

alluvial deposits (ALLUVIO) and of massive sand-

stone (AR_BIS), and the presence of uncultivated or

abandoned land (INC).

Fig. 8 allows for a comparison of the models

performance. By upgrading the landslide inventory,

the total number of mapping units correctly classified,

a measure of the model fit (Chung and Fabbri, 2003),

increases from 74.2% to 78.9%. This indicates that a

more complete inventory improves the model fit.

However, we note that the enhancement is not very

large (4.7%), indicating that even the susceptibility

model prepared using solely the 1955 landslide inven-

tory is sufficiently robust as to explain the known

distribution of the post-1955 slope failures. By adding

new landslides, the number of stable mapping units

that are correctly classified increases 1.6%, less than

the number of unstable slope units wrongly attributed

to the stable class, which decreases 5%. Correspond-

ingly, the number of misclassified stable mapping

units decreases less than the misclassified unstable

units. By adding the landslides mapped in the 1999

inventory (E1–E2 in Table 2) the model performance

does not change. We attribute it to the small number

of new landslides in the 1999 map (57), and to the

performance of the model. A relevant proportion

(50% in number, 84% in area) of the new landslides

in the period 1994–1999 (E1–E2) occurred on S–SW

facing slopes (Fig. 3E). This may explain why the

only difference between the variables entered in the

1994 model and those entered into the 1999 model is

the absence of variable TR2 (slope unit facing S–SE)

and the presence of variable TR3 (slope unit facing S–

SW) (Table 4).

Information is available to attempt a quantitative

validation of the susceptibility model. To accomplish

this, we compute the total area of new landslides (at

the date of the photographs) in each mapping unit.

We then compare the results with the susceptibility

zoning obtained by the different discriminant models

(Fig. 7). Fig. 9 shows, on the x-axis the probability

of landslide spatial occurrence, (i.e. susceptibility,

ranked from most to least susceptible), and on the

y-axis the percentage of landslide area in each sus-

ceptibility class. In the Figure, the four curves are

similar, but provide different information. Curves I

and II relate the percentage of landslide are used to

prepare the model (past landslides, A1–A2 for model

A, and A1–E2 for model B) to the predicted suscept-

ibility. Curves III and IV relate the cumulative per-

centage of landslide occurred bafter the model was

preparedQ, to the model prediction. While the curves

I and II measure model fit, curves III and IV provide

a quantitative measure of the model ability to predict

future landslides geographically, a form of model

validation (Chung and Frabbri, 1999; Remondo et

al., 2003). As expected, model fit is better than

model performance, which decreases with the

increase of the time span of the prediction. We

attribute the improved performance of the model

(e.g. from model III to IV) chiefly to the augmented

number of landslides (from 1719, 40.76 km2 to

2722, 47.39 km2).

Table 5 shows similar results. In each row, corre-

sponding to a different susceptibility model, the table

lists the percentage and the total landslide area (in

square kilometres) mapped in a given period that falls

in 5 classes of landslide susceptibility, from very high

(VH) to very low (VL). The first block of numbers

(percentage and total area) in each row compares the

model forecast with the sub-set of landslides mapped

as active in the same set of aerial photographs used to

obtain the inventory used for the production of the

model. The remaining blocks show how well a model

was capable of predicting future landslides. Inspection

of the table reveals that all the models correctly

classified as dlandslide proneT most the areas where

active landslides were identified, and most of the areas

where future (with respect to the model) landslides

occurred. As an example, for model A (first row in

Table 5), which was prepared using landslides

obtained by interpreting the 1955 aerial photography

(A1–A2 in Table 2), the first block shows that 79% of

all landslides recognized as active in 1955 occurred

within high (H, 30%) and very high (VH, 49%)

susceptibility zones, and only 9% in low (L, 8%)

and very low (VL, 1%) susceptibility areas. Model

A performs less efficiently when it comes to predict

the landslides occurred in the period from 1955 to

1975 (B1–B2 in Table 2). The model was capable of

correctly predicting 75% of the new landslides, but

Table 4

Variables entered into the five discriminant models (see Fig. 7)

Variable description Variable Model SDFC

Model A1 Model B2 Model C3 Model D4 Model E5

Drainage channel magnitude MAGN – 0.126 0.117 0.124 0.124

Drainage channel order ORDER 0.218 0.288 0.260 0.232 0.232

Drainage channel length LINK_LEN 0.065 0.180 0.150 0.119 0.119

Slope unit contributing area AREAT_C 0.083 – – – –

Slope unit area SLO_AREA 0.282 0.162 0.191 0.246 0.246

Slope unit micro-relief R 0.177 0.125 0.133 0.139 0.139

Slope unit mean elevation ELV_M – – – 0.097 0.097

Slope unit mean terrain gradient SLO_ANG 0.919 0.470 1.754 1.456 1.456

Slope unit mean terrain gradient squared SLO_ANG2 1.116 1.165 1.236 1.265 1.265

Slope unit terrain gradient standard deviation ANG_STD 0.092 0.200 0.205 0.190 0.190

Drainage channel mean slope LNK_ANG 0.239 0.284 0.267 0.286 0.286

Slope unit length SLO_LEN 0.087 0.078 0.065 – –

Slope unit length standard deviation LEN_STD – 0.079 0.066 0.125 0.125

Slope unit terrain gradient (lower portion) ANGLE1 – 0.287 0.178 – –

Slope unit terrain gradient (middle portion) ANGLE2 0.312 – 0.437 0.186 0.186

Slope unit terrain gradient (upper portion) ANGLE3 0.246 0.427 – – –

Concave profile down slope CONV 0.164 0.204 0.211 0.208 0.208

Concave–convex profile COV_COC 0.048 – – 0.051 0.051

Convex–concave profile COC_COV 0.115 0.129 0.135 0.150 0.150

Rectilinear slope profile RET 0.066 0.047 0.064 0.048 0.048

Complex slope profile CC 0.334 0.272 0.245 0.200 0.200

Argillitic unit AG_VA_PA 0.133 – – – –

Zebedassi limestone ALB_ZEB 0.072 – – – –

Recent alluvial deposit ALLUVIO 0.694 0.584 0.571 0.592 0.592

Monte Vallassa sandstone AR_BIS 0.427 0.388 0.397 0.441 0.441

Ranzano sandstone AR_R_M_P 0.071 0.059 0.052 0.065 0.065

Scabiazza sandstone AR_SCA – 0.060 0.056 0.063 0.063

Chaotic complex AT_PA_CA 0.219 – – – –

Detritus DETRITO 0.081 0.077 0.094 0.099 0.099

Monte Lumello marl MR_AN_LO 0.293 0.130 0.122 0.146 0.146

Rigoroso marl MR_B_R_C 0.119 0.093 0.092 0.129 0.129

Bosmenso marl MR_BOSM 0.108 0.062 0.044 0.051 0.051

Monte Piano marl MR_P_R_B 0.118 0.109 0.107 0.122 0.122

Cassano–Spinola conglomerate SACONG 0.097 0.030 0.029 – –

Bare rock or soil ALV – 0.055 0.064 0.085 0.085

Dense forest BD 0.052 0.052 0.053 0.048 0.048

Woods BMD – – – 0.038 0.038

Uncultivated area INC 0.212 0.273 0.292 0.281 0.281

Pasture PRA 0.176 0.192 0.199 0.222 0.222

Cultivated area SEM 0.184 0.246 0.285 0.277 0.277

Bedding dipping into the slope REG 0.182 0.119 0.111 0.078 0.078

Bedding dipping out of the slope FRA 0.101 – – – –

Chaotic bedding attitude CAO 0.059 – – – –

Slope unit facing N–NE TR1 0.129 0.079 0.065 0.073 0.126

Slope unit facing S–SE TR2 – – 0.037 0.042 –

Slope unit facing S–SW TR3 – – – – 0.053

Very old (relict) landslide (A0) FRA_OLD 0.092 0.061 0.062 0.053 0.053

(1) Model A obtained using landslides A1–A2 (Fig. 7A).

(2) Model B obtained using landslides A1–B2 (Fig. 7B).

(3) Model C obtained using landslides A1–C2 (Fig. 7C).

(4) Model D obtained using landslides A1–D2 (Fig. 7D).

(5) Model E obtained using landslides A1–E2 (Fig. 7E).

Variables with large standard discriminant function coefficients (SDFC), in absolute value, are shown in bold.


80.083.9 83.8 85.0 85.0

74.277.0 77.7 78.9 78.9

67.4 67.1 68.4 69.0 69.0

20.016.1 16.2 15.0 15.0

32.6 32.9 31.6 31.0 31.0

0

10

20

30

40

50

60

70

80

90

100

Perc

enta

ge o

f M

appi

ng U

nits

A1–A2 A1–B2 A1–C2 A1–D2 A1–E2

Fig. 8. Degree of fit of the five landslide susceptibility models. In the graph, x-axis shows landslide inventories used in the analysis (see also

Table 2), and y-axis shows percentage of mapping units. Large black circles: overall percentage of mapping units correctly classified by the 5

susceptibility models. Grey and open symbols show mapping units correctly and incorrectly classified, respectively. Grey diamonds show

percentage of mapping units free of landslides classified as stable. Grey squares show percentage of mapping units having landslides classified

as unstable. Open diamonds show percentage of mapping units free of landslides misclassified as unstable (type 1 errors). Open squares show

percentage of mapping units having landslides misclassified as stable (type 2 errors).


failed to predict 12% of the slope failures that

occurred in low (9%) and in very low (3%) suscept-

ibility areas. Note that the percentage of landslides

falling in the very high susceptibility (34%) class is

lower than the percentage in the high susceptibility

class (41%), an indication of the reduced performance

of the model. Performance of model A decreases

further if one considers the landslides occurred after

1975. In particular, the model A was capable of pre-

dicting bonlyQ 54% of the landslides identified in the

period 1994–1999 (E1–E2 in Table 2), with a consid-

erable proportion of slope failures (31%) occurring in

the unclassified (U) susceptibility class. Considering

the complexity of the Staffora basin, and the limited

number of landslides that occurred in the period (57),

we regard the model performance as very good. Data

in Table 5 can also be used to determine the contribu-

tion of new landslides to the model performance.

Considering the last column, one can see that model

A was capable of predicting 54% of the landslides

occurred in the period 1994–1999 (E1–E2 in Table 2),

and model D correctly predicted 98% of the landslides

in the same period, with the majority of the slope

failures (84%) falling in the very high susceptibility

class and none of the failures occurring in the very

low susceptibility class.

In conclusion, we take the outcome of the last

discriminant model (Fig. 7E) as a quantitative mea-

sure of the spatial probability of the landslides in the

Staffora basin, and we use it to determine landslide

hazard in the catchment.

4.5. Landslide hazard

We now have all the information to determine

quantitatively landslide hazard in the Staffora

basin. Fig. 10 summarizes the adopted workflow.

We use:

(i) the probability of landslide size, a proxy for

landslide magnitude, obtained from the statisti-

cal analysis of the frequency–area distribution

of the mapped landslides (Eqs. (5) and (6) and

Fig. 4),

(ii) the probability of landslide occurrence for

established periods, obtained by computing

the mean recurrence interval between succes-

sive failures in each mapping unit, and adopt-

ing a Poisson probability model (Eq. (9) and

Fig. 5), and

(iii) the spatial probability of slope failures (i.e.

susceptibility) obtained through discriminant

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

I

II

III

IV

Percentage of study area in the susceptibility classes

Perc

enta

ge o

f la

ndsl

ide

area

in th

e su

scep

tibili

ty c

lass

es

most susceptible least susceptible

Fig. 9. Graph comparing model fit and model performance (prediction rate). In the graph, the x-axis shows the probability of landslide spatial

occurrence (susceptibility), ranked from most (left) to least (right) susceptible, and y-axis shows the percentage of landslide area in each

susceptibility class. Curve I and II illustrate model fit. Curve I shows the ability of the model obtained using landslides identified in the period

A1–A2 (Table 2) to forecast the same set of landslides. Curve II shows the capacity of the model prepared using landslides in the period A1–E2 to

forecast recent landslides identified in the 1999 aerial photographs (E1–E2). Curve III and IV illustrate model performance. Curve III indicates

the ability of the model prepared using landslides identified in the period A1–A2 to forecast bfutureQ landslides occurred in the period B1–E2.

Curve IV indicates the ability of the model prepared using landslides identified in the period A1–B2 to forecast bfutureQ landslides occurred in

the period C1–E2.


analysis of 46 environmental variables (Eq. (13)

and Fig. 7).

Assuming independence (Eq. (2)), we multiply the

three probabilities and we obtain landslide hazard, i.e.

the joint probability that a mapping unit will be

affected by future landslides that exceed a given

size, in a given time, and because of the local envir-

onmental setting. Fig. 11 shows examples of the land-

slide hazard assessment. The figure portrays landslide

hazard for mapping units in the central part of the

Staffora river basin, for four periods (5, 10, 25 and 50

years), and for two different landslide sizes, greater or

equal than 2000 m2, and greater or equal than 10,000

m2 (1 ha).

5. Discussion of the results

The proposed method allowed us to determine

quantitatively landslide hazard in the Staffora River

basin. We obtained most of the information used in

the analysis from a detailed multi-temporal inven-

tory map. Production of the multi-temporal in-

ventory required a total of 6 months of three

geomorphologists. Digitization and validation of

the map required a total of one month of two GIS

experts. Statistical analysis and hazard modelling

required three weeks of two geomorphologists. Con-

sidering the thematic information used to ascertain

susceptibility (i.e., DTM, geology, land use) was

already available in digital format (Antonini et al.,

Table 5

Validation of susceptibility models

Susceptibility class Landslide set and age

A1–A2 B1–B2 C1–C2 D1–D2 E1–E2

% km2 % km2 % km2 % km2 % km2

Model A Fig. 7A VH 49 1.21 34 2.21 38 1.22 36 1.22 17 0.18

H 30 0.74 41 2.70 38 1.23 44 1.46 37 0.39

U 12 0.30 13 0.85 15 0.48 12 0.39 31 0.32

L 8 0.20 9 0.62 8 0.26 7 0.24 13 0.13

VL 1 0.01 3 0.19 1 0.05 1 0.04 2 0.02

Model B Fig. 7B VH 73 3.21 73 2.36 73 2.46 70 0.73

H 18 0.81 20 0.65 20 0.67 24 0.25

U 3 0.15 4 0.13 2 0.06 4 0.04

L 4 0.16 2 0.08 4 0.13 2 0.02

VL 2 0.07 1 0.02 1 0.03 0 0.00

Model C Fig. 7C VH 72 1.72 74 2.50 70 0.73

H 22 0.53 19 0.64 24 0.25

U 3 0.09 2 0.06 4 0.04

L 2 0.04 4 0.13 2 0.02

VL 1 0.02 1 0.02 0 0.00

Model D Fig. 7D VH 84 1.15 84 0.87

H 11 0.15 14 0.15

U 2 0.02 0 0.00

L 3 0.04 2 0.02

VL 0 0.00 0 0.00

Model E Fig. 7E VH 80 0.68

H 19 0.16

U 0 0.00

L 1 0.01

VL 0 0.00

Susceptibility classes are: VH, very high [1.0–0.8]; H, high [0.8–0.6]; U, uncertain [0.6–0.4]; L, low [0.4–0.2]; and VL, very low [0.0–0.2]. See

text for explanation.


2000; Ardizzone et al., 2002), production of the

multi-temporal inventory was the most difficult

and time consuming-operation.

The proposed probability model allows for its

temporal verification. Providing an estimate of the

period of landslide hazard, the forecast is verifiable

at any moment in time, provided accurate information

on landslides is available. This can be obtained by

systematically compiling information on landslide

occurrence, and particularly after each main land-

slide-triggering event (i.e. a heavy rainstorm, a pro-

longed rainfall period, a snowmelt event, or an

earthquake). When new information on landslides

becomes available, new spatial (S), temporal (PN)

or size (PAL) models can be prepared, and the hazard

model revised.

The proposed landslide hazard model holds

under a set of assumptions, namely: (i) landslides

will occur in the future under the same circum-

stances and because of the same factors that pro-

duced them in the past; (ii) landslide events are

independent (uncorrelated) random events in time;

(iii) the mean recurrence of slope failures will

remain the same in the future as it was observed

in the past; (iv) the statistics of landslide area are

correct and will not change in the future; (v) land-

slide area is a reasonable proxy for landslide mag-

nitude; and (vi) the probability of landslide size, the

probability of landslide occurrence for established

periods, and the spatial probability of slope failures,

are independent. We now discuss these assumptions

for the Staffora basin.

That landslides will occur in the future under the

same conditions and because of the same factors

that triggered them in the past is a recognized

postulate for all functional (statistically based) sus-

Environmental ThematicVariables

Multi-temporal landslideinventory map

(Figure 3)

Susceptibilityassessment(Figure 7E)

“Where”

DiscriminantAnalysis(eq. 16)

Exceedanceprobability(Figure 5)“When”

Poisson model(eqs. 7, 8, 9)

Probability oflandslide area(Figure 4 A-B)“How large”

Inverse GammaDouble Pareto(eqs. 4, 5, 6)

DATA MODELS RESULTS

Landslide HazardAssessment(Figure 11)

Fig. 10. Block diagram exemplifying the work flow adopted to determine landslide hazard. Rectangles indicate input data. Diamonds indicate

individual models, for landslide susceptibility, for the temporal probability of landslides, and for landslide size. Ellipses indicate intermediate

results. Hexagon indicates the final result.


ceptibility assessments (Carrara et al., 1991; Hutch-

inson, 1995; Aleotti and Chowdhury, 1999; Chung

and Frabbri, 1999; Guzzetti et al., 1999). We dis-

cussed the general limitations of this assumption

when we presented the susceptibility model. We

will now focus on the validity of the postulate in

the Staffora basin.

The difficulty with the principle of uniformitarian-

ism lays in the fact that the environmental conditions

(predisposing factors) that caused landslides bmust

remain the same in the futureQ in order to cause

similar slope failures. Our hazard model has an

expected validity of 50 years. The problem is to

investigate the possibility that the predisposing fac-

tors will change in the considered period. It is safe to

assume that geological factors (e.g. lithology, struc-

ture, seismicity) will not change (significantly) in

such a short time. Local morphological modifications

are possible in the period, due chiefly to stream

erosion, landslides and human actions, but extensive

(widespread) morphological changes are not foresee-

able. Inspection of Table 4 indicates that 42 of the 47

thematic variables entered into the susceptibility

model are not expected to change significantly in

the considered period. However, other variables and

most notably land use types may change significantly

in the period. Qualitative estimates indicate a reduc-

tion of about 25% of the forest coverage in the period

from 1955 to 2000, in favour of cultivated land. In

the same period, agricultural practices have changed,

largely aided by large and powerful mechanical

equipment. In the central and southern Apennines,

areas recently deforested for agricultural purposes

are more prone to shallow landslides (Cardinali et

al., 2000). If this will be the case for the Staffora

basin, some of the environmental variables consid-

ered in the susceptibility model will change, possibly

hampering the validity of the model, and new vari-

ables showing areas of land use change should be

considered to describe the initiation of shallow slope

failures. We note that the susceptibility model does

not consider the landslide triggering factors, i.e. rain-

5 years

0 1 km

Landslide size≥ 2,000 m2

Landslide size≥ 10,000 m2

10 years

25 years

50 years

Fig. 11. Examples of landslide hazard maps for four periods, from 5

to 50 years (from top to bottom), and for two landslide sizes,

ALz2000 m2 (left) and ALz10,000 m2 (right). Shades of gray

show different joint probabilities of landslide size, of landslide

temporal occurrence, and of landslide spatial occurrence (suscept-

ibility). For improved readability, the scales of landslide hazard

differ for the two landslide sizes.


fall, seismic shaking or snow melting. Changes in the

frequency or intensity of the driving forces will not

affect (at least not in the considered period) the

susceptibility model. However, it may affect the rate

of occurrence of landslide events.

In the Apennines, evidence exists that where abun-

dant clay, marl and sandstone crop out, landslides

exhibit spatial persistence, i.e. they tend to occur

where they have occurred in the past (Cardinali et

al., 2000). If this is the case for the Staffora River

basin, the assumption that landslide events are uncor-

related random events in time will be violated. Ana-

lysis of the multi-temporal inventory map (Fig. 3)

indicates that in the study area 40% of all the land-

slides identified in the period from 1955 to 1999 (A2–

E2 in Table 2) occurred inside landslides mapped on

the 1955 aerial photographs (A0–A1 in Table 2).

Considering only the 2390 landslides occurred in the

45-year period from 1955 to 1999 (A2–E2 in Table 2),

12% of the slope failures occurred in the same area of

other landslides triggered in the same period. Analysis

of the historical record of damaging landslides indi-

cates that the 389 events listed in the catalogue

occurred at 332 different sites, with only 38 sites

affected two or more times. The same bsiteQ was

affected on average 1.2 times, indicating a low rate

of recurrence of events at the same site. All this

concurs to establish that for the period of our hazard

assessment (50 years), in the Staffora River basin

landslides can be considered uncorrelated random

events in time.

Analysis of the record of damaging landslides

reveals that of the 248 events (63.7%, 96.0% of

which after 1950) for which the triggering mechan-

ism is known, 210 (84.7%) were the result of intense

rainfall, 16 (6.5%) to a combination of intense rain-

fall and snow melting, infiltration, irrigation or bro-

ken pipes, 14 (5.6%) to erosion at the base of the

slope, and eight (3.2%) to other causes. Earthquake-

induced landslides were not reported. The analysis

indicates that most of the landslides in the Staffora

River basin are rainfall-induced. If the rate of occur-

rence of the meteorological events that trigger land-

slides changes, the mean rate of slope failures will

also change. If the intensity (amplitude and duration)

of the rainfall will change, the rate of slope failures

might change, in a way that is not easily predictable.

For the coming decades, south of the Alps models

of global climate change forecast the same total

amount of yearly rainfall concentrated in a fewer

number of high intensity events (Bradley et al.,

1987; Brunetti et al., 2000; Easterling et al., 2000;

IPCC, 2001). This may result in more abundant


shallow landslides, and in less frequent deep-seated

slope failures (Buma and Dehn, 1998; Malet et al.,

2005). Modifications in land use induced by changes

in agricultural practices may also change the rate of

occurrence of landslides.

Determining the statistics of landslide areas is no

trivial task (Malamud et al., 2004). Only a handful of

inventories are available which are substantially

complete and have enough cartographic detail to

allow for determining unambiguously the PDF of

landslide areas (Stark and Hovius, 2001; Guzzetti

et al., 2002a,b; Guthrie and Evans, 2004a,b; Mala-

mud et al., 2004). The (scant) available information

indicates that the frequency–area statistics of land-

slide areas does not change significantly across litho-

logical or physiographical boundaries. Malamud et

al. (2004) showed that three different populations of

landslides produced by different triggers (i.e. seismic

shaking, intense rainfall, rapid snow melting) in

different physiographical regions (southern Califor-

nia, central America, central Italy), exhibit virtually

identical PDFs. Unpublished work conducted in cen-

tral Italy indicates that for the same physiographical

region the PDF of landslide area does not change in

time. It is, therefore, safe to assume that in the

Staffora River basin the frequency–area statistics of

landslide area will not change in the period of the

hazard assessment. It is also justified to use a single

PDF for the entire basin. Since the most abundant

landslides in the catchment are small (~2000 m2, Fig.

4A), great care must be taken in mapping accurately

(and completely) the small slope failures. The slope

of the heavy tail of the PDF in Fig. 4A is controlled

by a limited number of landslides. There are 16

landslides larger than 50,000 m2 (5 ha) and only

one landslide larger than 100,000 m2 (10 ha). Care

must be taken in mapping the largest landslides, and

in deciding whether they represent an individual

slope failure or the result of two or more coalescent

landslides.

Hungr (1997) argued that no unique measure of

landslide magnitude is available, and proposed to

adopt destructiveness as measure of landslide mag-

nitude. In this work, we have taken landslide area as

a proxy for landslide destructiveness (and of land-

slide magnitude). We obtained the area of the in-

dividual slope failures from the multi-temporal

landslide inventory in GIS format. However, is land-

slide area a good measure of landslide destructiveness

in the Staffora basin? Analysis of the historical cat-

alogue of damaging slope failures reveals that infor-

mation on the size (area, length and width) of

landslides is available for 26 events (6.7%), which

range from 600 m2 to 600,000 m2 (mean=58,000 m2,

std. dev.=13,500 m2). Damage caused by these land-

slides was mostly to the road network and, sub-

ordinately, to private homes and to the aqueduct.

Casualties were not reported. Information on the land-

slide type is available for 28 events (7.2%), of which

15 were slides, 6 flows and 5 falls. Slides and flows

caused the most severe damage, and falls produced

only minor interruptions along the roads. Information

on landslide velocity is available for five events, and

ranges from 1.2�101 to 5.8�103 mm/s (moderate

landslide velocity (Cruden and Varnes, 1996)). As a

whole, the available historical information on dama-

ging slope failures suggests that: (i) damage in the

Staffora River basin is caused mostly by slow to

rapid moving slides and flows, i.e. the type of failures

considered in the hazard assessment, and (ii) large

landslides tend to produce larger damage, particularly

to roads.

The last assumption of the proposed model is that

the probabilities of landslide size, of temporal occur-

rence, and of spatial incidence of mass movements are

independent. The legitimacy of this assumption is

difficult to prove quantitatively. We have shown that

the probability of landslide area is largely independent

from the physiographical setting. As a first-approxi-

mation, it is safe to conclude that the probability of

landslide area is independent from susceptibility. The

susceptibility model was constructed without consid-

ering the driving forces (meteorological or else) that

control the rate of occurrence of slope failures in the

Staffora River basin. We conclude that the rate of

landslide events is independent from susceptibility.

The catalogue of historical damaging landslides

reveals that landslides occurred in all sizes. We con-

sider this an indication that the rate of failures is

independent from landslide size.

Finally, the main scope of a landslide hazard

assessment is to provide quantitative expertise on

future slope failures to planners, decision-makers,

civil defence authorities, insurance companies, land

developers, and individual landowners. The pro-

posed method allowed us to prepare a large number


of different hazard maps (Fig. 11), depending on the

adopted susceptibility model, the established period,

and the minimum size of the expected landslide.

How to combine such a large number of hazard

maps efficiently, producing cartographic, digital, or

thematic products useful for the large range of inter-

ested users, remains an open problem that needs

investigation.

6. Conclusions

We have proposed a probabilistic model to ascer-

tain landslide hazard that fulfils the definition of

landslide hazard given by Varnes and the IAEG

Commission on Landslides and other Mass-Move-

ments (1984), amended by Guzzetti et al. (1999) to

include the magnitude of the landslide event. The

model expresses landslide hazard as the joint prob-

ability of landslide size, considered a proxy for land-

slide magnitude, of landslide occurrence in an

established period of time, and of landslide spatial

occurrence given the local environmental setting. We

tested the model in the Staffora River basin, for

which we obtained a quantitative estimate of land-

slide hazard. We obtained most of the information

used to determine landslide hazard from a detailed

multi-temporal inventory map. The model proved

applicable in the test area, and we believe is ap-

propriate in similar areas, chiefly where a multi-

temporal landslide inventory captures the types,

sizes, and expected recurrence of slope failures.

Improvements to the model may include a more

robust definition of the spatial probability of land-

slide occurrence, a better temporal model, and im-

proved number-size statistics, particularly for the

smallest landslides. Lastly, in this exercise we have

prepared tens of different hazard maps. How to com-

bine such a large number of maps efficiently, produ-

cing outputs useful for planners and decision-makers

remains an open problem.

Acknowledgements

We acknowledge the help of Florisa Melone in

formalizing the hazard model. We are grateful to

Bruce Malamud for reviewing the paper. Work sup-

ported by CNR GNDCI (publication number 2887)

and CNR IRPI grants. Early part of the work con-

ducted under contract from the Regione Lombardia.

References

Aleotti, P., Chowdhury, R., 1999. Landslide hazard assessment:

summary review and new perspectives. Bulletin of Engineering

Geology and the Environment 58, 21–44.

Antonini, G., Ardizzone, F., Cardinali, M., Carrara, A., Detti, R.,

Galli, M., Guzzetti, F., Reichenbach, P., Sotera, M., Tonelli,

G., 2000. Rapporto conclusivo: tecniche e metodologie idonee

alla produzione di carte della pericolosita e del rischio da

frana in aree campione rappresentative del territorio della

regione Lombardia. CNR IRPI unpublished report, 139 p.

(in Italian).

Ardizzone, F., Cardinali, M., Carrara, A., Guzzetti, F., Reichenbach,

P., 2002. Uncertainty and errors in landslide mapping and land-

slide hazard assessment. Natural Hazards and Earth System

Science 2 (1–2), 3–14.

Atckinson, P.M., Massari, R., 1998. Generalised linear modelling of

susceptibility lo landsliding in the Central Apennines, Italy.

Computers & Geosciences 24 (4), 373–385.

Ayalew, L., Yamagishi, H., 2005. The application of GIS-based

logistic regression for landslide susceptibility mapping in the

Kakuda–Yahiko Mountains, Central Japan. Geomorphology 65

(1–2), 15–31.

Ayalew, L., Yamagishi, H., Ugawa, N., 2004. Landslide suscept-

ibility mapping using GIS-based weighted linear combination,

the case in Tsugawa area of Agano River, Niigata Prefecture,

Japan. Landslides 1 (1), 73–81.

Baeza, C., Corominas, J., 2001. Assessment of shallow landslide

susceptibility by means of multivariate statistical techniques.

Earth Surface Processes and Landforms 26 (12), 1251–1263.

Binaghi, E., Luzi, L., Madella, P., Pergalani, F., Rampini, A., 1998.

Slope instability zonation: a comparison between certainty fac-

tor and Fuzzy Dempster–Shafer approaches. Natural Hazards

17, 77–97.

Bonham-Carter, G.F., 1991. Integration of geosceintic data using

GIS. In: Goodchild, M.F., Rhind, D.W., Maguire, D.J. (Eds.),

Geographic Information Systems: Principle and Applications.

Longdom, London, pp. 171–184.

Brabb, E.E., 1984. Innovative approach to landslide hazard and risk

mapping. Proceedings of the 4th International Symposium on

Landslides, Toronto, vol. 1, pp. 307–324.

Bradley, R.S., Diaz, H.F., Eischeid, J.K., Jones, P., Kelly, P., Good-

ess, C., 1987. Precipitation fluctuations over Northern Hemi-

sphere land areas since the mid-19th Century. Science 237,

171–175.

Brunetti, M., Buffoni, L., Maugeri, M., Nanni, T., 2000. Precipita-

tion intensity trends in Northern Italy. International Journal of

Climatology 20, 1017–1032.

Bucknam, R.C., Coe, J.A., Chavarria, M.M., Godt, J.W., Tarr, A.C.,

Bradley, L.-A., Rafferty, S., Hancock, D., Dart, R.L., Johnson,

M.L., 2001. Landslides triggered by Hurricane Mitch in Guate-


mala — inventory and discussion. U.S. Geological Survey Open

File Report 01-443 (38 pp.).

Buma, J., Dehn, M., 1998. A method for predicting the impact of

climate change on slope stability. Environmental Geology 35

(2–3), 190–196.

Cardinali, M., Ardizzone, F., Galli, M., Guzzetti, F., Reichenbach,

P., 2000. Landslides triggered by rapid snow melting: the

December 1996–January 1997 event in Central Italy. In:

Claps, P., Siccardi, F. (Eds.), Proceedings 1st Plinius Con-

ference on Mediterranean Storms. Bios Publisher, Cosenza,

pp. 439–448.

Cardinali, M., Carrara, A., Guzzetti, F., Reichenbach, P., 2002a.

Landslide hazard map for the Upper Tiber River basin.

CNR GNDCI Publication number 2116, map at 1 :100,000

scale.

Cardinali, M., Reichenbach, P., Guzzetti, F., Ardizzone, F.,

Antonini, G., Galli, M., Cacciano, M., Castellani, M., Sal-

vati, P., 2002b. A geomorphological approach to estimate

landslide hazard and risk in urban and rural areas in Umbria,

central Italy. Natural Hazards and Earth System Science 2

(1–2), 57–72.

Carrara, A., 1983. A multivariate model for landslide hazard eva-

luation. Mathematical Geology 15, 403–426.

Carrara, A., Cardinali, M., Detti, R., Guzzetti, F., Pasqui, V., Reich-

enbach, P., 1991. GIS techniques and statistical models in

evaluating landslide hazard. Earth Surface Processes and Land-

form 16 (5), 427–445.

Carrara, A., Cardinali, M., Guzzetti, F., 1992. Uncertainty in asses-

sing landslide hazard and risk. ITC Journal 2, 172–183.

Carrara, A., Cardinali, M., Guzzetti, F., Reichenbach, P., 1995. GIS

technology in mapping landslide hazard. In: Carrara, A., Guz-

zetti, F. (Eds.), Geographical Information Systems in Assessing

Natural Hazards. Kluwer Academic Publisher, Dordrecht, The

Netherlands, pp. 135–175.

Carrara, A., Crosta, G.B., Frattini, P., 2003. Geomorphological and

historical data in assessing landslide hazard. Earth Surface

Processes and Landforms 28 (10), 1125–1142.

Cevik, E., Topal, T., 2003. GIS-based landslide susceptibility map-

ping for a problematic segment of the natural gas pipeline,

Hendek (Turkey). Environmental Geology 44 (8), 949–962.

Chung, C.J., Frabbri, A.G., 1999. Probabilistic prediction models

for landslide hazard mapping. Photogrammetric Engineering

and Remote Sensing 65 (12), 1389–1399.

Chung, C.J., Fabbri, A.G., 2003. Validation of spatial prediction

models for landslide hazard mapping. Natural Hazards 30 (3),

451–472.

Chung, C.J., Fabbri, A.G., 2005. Systematic procedures of landslide

hazard mapping for risk assessment using spatial prediction

models. In: Glade, C.J., et al., (Eds.), Landslide Risk Assess-

ment. John Wiley, pp. 139–174.

Coe, J.A., Michael, J.A., Crovelli, R.A., Savage, W.Z., 2000. Pre-

liminary map showing landslide densities, mean recurrence

intervals, and exceedance probabilities as determined from his-

toric records, Seattle, Washington. United States Geological

Survey Open File Report 00-303.

Connor, C.B., Hill, B.E., 1995. Three nonhomogeneous Poisson

models for the probabilita of basaltic volcanism: application to

the Yucca Mountain region, Nevada. Journal of Geophysical

Research 100, 10107–10125.

Costa, J.A., Baker, V.R., 1981. Surficial Geology — Building with

the Earth. John Wiley and Sons, New York. 498 pp.

Crovelli, R.A., 2000. Probability models for estimation of number

and costs of landslides. United States Geological Survey Open

File Report 00-249.

Cruden, D.M., Varnes, D.J., 1996. Landslide types and processes.

In: Turner, A.K., Schuster, R.L. (Eds.), Landslides, Investigation

and Mitigation, Special Report, vol. 247. Transportation

Research Board, Washington, D.C, pp. 36–75.

Dai, F.C., Lee, C.F., 2002. Landslide characteristics and slope

instability modelling using GIS, Lantau Island, Hong Kong.

Geomorphology 42, 213–228.

Dai, F.C, Lee, C.F., 2003. A spatiotemporal probabilistic modelling

of storm-induced shallow landsliding using aerial photographs

and logistic regression. Earth Surface Processes and Landforms

28 (5), 527–545.

Detti, R., Pasqui, V., 1995. Vector and raster structures in generating

drainage-divide networks from Digital Terrain Models. In: Car-

rara, A., Guzzetti, F. (Eds.), Geographical Information Systems

in Assessing Natural Hazards. Kluwer Academic Publisher,

Dordrecht, The Netherlands, pp. 35–55.

Easterling, D.R., Meehl, G.M., Parmesan, C., Changnon, S.A., Karl,

T.R., Mearns, L.O., 2000. Climate extremes: observations, mod-

eling, and impacts. Science 289, 2068–2074.

Fabbri, A.G., Chung, C.J., Cendrero, C., Remondo, J., 2003. Is

prediction of future landslides possible with a GIS? Natural

Hazards 30 (3), 487–503.

Guthrie, R.H., Evans, S.G., 2004a. Magnitude and frequency of

landslides triggered by a storm event, Loughborough Inlet,

British Columbia. Natural Hazards and Earth System Science

4, 475–483.

Guthrie, R.H., Evans, S.G., 2004b. Analysis of landslide frequen-

cies and characteristics in a natural system, coastal British

Columbia. Earth Surface Processes and Landforms 29 (11),

1321–1339.

Guzzetti, F., 2002. Landslide hazard assessment and risk evaluation:

overview, limits and prospective. Proceedings 3rd MITCH

Workshop Floods, Droughts and Landslides — Who Plans,

Who Pays, pp. 24–26. November 2002, Potsdam, available at

http://www.mitch-ec.net/workshop3/Papers/paper_guzzetti.pdf.

Guzzetti, F., Carrara, A., Cardinali, M., Reichenbach, P., 1999.

Landslide hazard evaluation: an aid to a sustainable develop-

ment. Geomorphology 31, 181–216.

Guzzetti, F., Reichenbach, P., Cardinali, M., Ardizzone, F., Galli, M.,

2002a. Impact of landslides in the Umbria Region Central Italy.

Natural Hazards and Earth System Science 3 (5), 469–486.

Guzzetti, F., Malamud, B.D., Turcotte, D.L., Reichenbach, P.,

2002b. Power-law correlations of landslide areas in Central

Italy. Earth and Planetary Science Letters 195, 169–183.

Harp, E.L., Jibson, R.L., 1996. Landslides triggered by the 1994

Northridge, California earthquake. Seismological Society of

America Bulletin 86, S319–S332.

Hovius, N., Stark, C.P., Allen, P.A., 1997. Sediment flux from a

mountain belt derived by landslide mapping. Geology 25,

231–234.

http://www.mitch%1Eec.net/workshop3/Papers/paper_guzzetti.pdf


Hungr, O., 1997. Some methods of landslide hazard intensity map-

ping. In: Cruden, D.M., Fell, R. (Eds.), Landslide Risk Assess-

ment. Balkema Publisher, Rotterdam, pp. 215–226.

Hutchinson, J.N., 1995. Keynote paper: landslide hazard assess-

ment. In: Bell, J.N. (Ed.), Landslides. Balkema, Rotterdam,

pp. 1805–1841.

Intergovernmental Panel on Climate Change, IPCC, 2001. Third

Assessment Report, Working Group I. Summary for policy-

makers. Available at: www.ipcc.ch.

Keaton, J.R., Anderson, L.R., Mathewson, C.C., 1988. Assessing

debris flow hazards on alluvial fans in Davis County, Utah. In:

Fragaszy, R.J. (Ed.), Proceedings 24th Annual Symposium on

Engineering Geology and Soil Engineering. Washington State

University, Pullman, pp. 89–108.

Klein, F.W., 1982. Patters of historical eruptions at Hawaiian vol-

canoes. Journal of Volcanology and Geothermal Research 12,

1–35.

Lee, S., 2004. Application of likelihood ratio and logistic regression

models to landslide susceptibility mapping using GIS. Environ-

mental Management 34 (2), 223–232.

Lee, S., Choi, J., Min, K., 2002a. Landslide susceptibility analysis

and verification using the Bayesian probability model. Environ-

mental Geology 43 (1–2), 120–131.

Lee, S., Chwae, U., Min, K., 2002b. Landslide susceptibility

mapping by correlation between topography and geological struc-

ture: the Janghung area, Korea. Geomorphology 46 (3–4),

149–162.

Lin, M.-L., Tung, C.C., 2004. A GIS-based potential analysis of the

landslides induced by the Chi-Chi earthquake. Engineering

Geology 71 (1–2), 63–77.

Lips, E.W., Wieczorek, G.F., 1990. Recurrence of debris

flows on an alluvial fan in central Utah. In: French, R.H.

(Ed.), Hydraulic/Hydrology of Arid Lands, Proceedings of the

International Symposium. American Society of Civil Engineers,

pp. 555–560.

Malamud, B.D., Turcotte, D.L., Guzzetti, F., Reichenbach, P., 2004.

Landslide inventories and their statistical properties. Earth Sur-

face Processes and Landforms 29 (6), 687–711.

Malet, J.-P., van Asch, T.H.W.J., van Beek, R., Maquaire, O., 2005.

Forecasting the behaviours of complex landslides with a spa-

tially distributed hydrological model. Natural Hazards and Earth

System Sciences 5 (1), 71–85.

Nagarajan, R., Roy, A., Vinod Kumar, R., Mukhetjess, A., Khire,

M.V., 2000. Landslide hazard susceptibility mapping based on

terrain and climatic factors for tropical monsoon regions.

Bulletin of Engineering Geology and the Environment 58 (4),

275–287.

Nathenson, M., 2001. Probabilities of volcanic eruptions and appli-

cation to the recent history of Medicine Lake Volcano. In:

Vecchia, A.V. (Ed.), U.S. Geological Survey Open-file Report

2001-324, pp. 71–74.

Olhmacher, G.C., Davis, J.C., 2003. Using multiple logistic regres-

sion and GIS technology to predict landslide hazard in northeast

Kansas, USA. Engineering Geology 69, 331–343.

Onoz, B., Bayazit, M., 2001. Effect of the occurrence process of the

peaks over threshold on the flood estimates. Journal of Hydrol-

ogy 244, 86–96.

Pelletier, J.D., Malamud, B.D., Blodgett, T., Turcotte, D.L., 1997.

Scale-invariance of soil moisture variability and its implications

for the frequency–size distribution of landslides. Engineering

Geology 48, 255–268.

Reger, J.P., 1979. Discriminant analysis as a possible tool in land-

slide investigations. Earth Surface Processes and Landforms 4,

267–273.

Regione Lombardia, 2002. Inventario delle frane e dei dissesti

idrogeologici della Regione Lombardia. Unita Operativa Dis-

sesti Idrogeologici, 2 CD-ROMs (in Italian).

Reichenbach, P., Galli, M., Cardinali, M., Guzzetti, F., Ardizzone,

F., 2005. Geomorphologic mapping to assess landslide risk:

concepts, methods and applications in the Umbria Region of

central Italy. In: Glade, P., et al., (Eds.), Landslide Risk Assess-

ment. John Wiley, pp. 429–468.

Remondo, J., Gonzalez, A., Diaz De Teran, J.R., Cendrero, A.,

Fabbri, A., Chung, C.F., 2003. Validation of landslide suscept-

ibility maps; examples and applications from a case study in

Northern Spain. Natural Hazards 30, 437–449.

Rossetti, R., 1997. Centri abitati instabili della Provincia di Pavia —

Vol. 1, CNR GNDCI Publication number 1780.

Rowbotham, D., Dudycha, D.N., 1998. GIS modelling of slope

stability in Phewa Tal watershed, Nepal. Geomorphology 26,

151–170.

Santacana, N., Baeza, B., Corominas, J., De Paz, A., Marturia,

J., 2003. A GIS-based multivariate statistical analysis for

shallow landslide susceptibility mapping in La Pobla de

Lillet Area (Eastern Pyrenees, Spain). Natural Hazards 30

(3), 281–295.

Servizio Geologico Nazionale, 1971. Carta Geologica d’Italia,

Foglio 71 Voghera, scale 1 :100,000.

Soeters, R., van Westen, C.J., 1996. Slope instability recognition

analysis and zonation. In: Turner, A.K., Schuster, R.L. (Eds.),

Landslide Investigation and Mitigation, Special Report, vol. 247.

National Research Council, Transportation Research Board,

pp. 129–177.

Stark, C.P., Hovius, N., 2001. The characterization of landslide size

distributions. Geophysics Research Letters 28 (6), 1091–1094.

Suzen, M.L., Doyuran, V., 2004. A comparison of the GIS based

landslide susceptibility assessment methods: multivariate versus

bivariate. Environmental Geology 45 (5), 665–679.

van Westen, C.J., 1994. In: Price, M.F., Heywood, D.I. (Eds.),

GIS in Landslide Hazard Zonation: a Review With Exam-

ples from the Colombian Andes. Taylor and Francis, Lon-

don, pp. 135–165.

Varnes, D.J., IAEG Commission on Landslides and other Mass-

Movements, 1984. Landslide Hazard Zonation: a Review of

Principles and Practice. NESCO Press, Paris. 63 pp.

Wieczorek, G.F., 1984. Preparing a detailed landslide-inventory

map for hazard evaluation and reduction. Bulletin Association

Engineering Geologists 21 (3), 337–342.

WP/WLI — International Geotechnical societies’ UNESCO Work-

ing Party on World Landslide Inventory, 1990. A suggested

method for reporting a landslide. International Association Engi-

neering Geology Bulletin 41, 5–12.



http://www.ipcc.ch


method for describing the activity of a landslide. International

Association Engineering Geology Bulletin 47, 53–57.



method for describing the rate of movement of a landslide.

International Association Engineering Geology Bulletin 52,

75–78.

Wu, S., Jin, Y., Zhang, Y., Shi, J., Dong, C., Lei, W., Shi, L., Tan,

C., Hu, D., 2004. Investigations and assessment of the landslide

hazards of Fengdu county in the reservoir region of the Three

Gorges project on the Yangtze River. Environmental Geology

45 (4), 560–566.

Yevjevich, V., 1972. Probability and Statistics in Hydrology. Water

Resources Publications, Fort Collins, Colorado. 302 pp.

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Probabilistic landslide hazard assessment at the basin scale