Hillslope
debris flows frequency
since the beginning of the 20th century
in the Massif des Ecrins (French Alps)
V. Jomelli & D. Brunstein
CNRS, UMR 8591, Meudonbellevue, France
C. Chochillon & P. Pech
Université Paris 1 PanthéonSorbonne, Paris, France
Keywords: frequency, dating methods, logistic regression, French alps 
ABSTRACT: The aim of this paper is firstly to characterise the debris flow frequency since the beginning of the 20^{th} century in 6 valleys located on the eastern part of the Massif des Ecrins (French Alps). This analysis is based on the dating of 142 debris flow deposits by lichenometry, dendrochronology, aerial photographs analysis from 1952 and old documents. Results show that it is very difficult to compare the two periods of 19001950 and 19502000 because the number of debris flows over the first half of the century is probably underestimated. Over the second period, the frequency of debris flow has decreased significantly for the 200399 m class lengths. We have also observed a decrease in the number of debris flows between 19501975 and 19752000. We have made two logistic regression models in order to determine an frequency probability according to geomorphological and climatic parameters. The first model shows that the frequency probability depends on the debris flow triggering zone altitude and the surface of the rock face, while the second model shows that the frequency probability depends on rainy events greater than 30 mm/day and also on the cumulated number of freezing days. 
Hillslope debris flow can be defined
as a rapid mass movement of a fast flowing mixture of sediment and water, which
is a very common phenomenon in the Alpine environment. Over the last few
decades special attention has been focused on the magnitude/frequency
variations of this process (Innes 1985, Rapp 1995). In the Alps Van Steijn
(1991, 1999) and Blijenberg (1998) have observed in the Bachelard Valley (south
of France) that activity has been vigorous since 1980 (especially in 1987) but
results do not necessarily point to a recent increase in debris flow activity.
In the Dolomites, Strunk (1992) says:“there is no evidence of any trend towards
an increase or a decrease in the frequency since the end of the last century”.
On the opposite Rebetez et al. (1997) have observed that the frequency of large
debris flows has increased since the late 1980s which could be due to an increase
in the number of intense rainfall events. Other researchers (Haeberli et al. 1990; Zimmerman & Haeberli
1992) show a relationship between the triggering of debris flows and glacier
retreat and permafrost degradation due to an increase in temperatures since the
middle of the 19^{th} century, a
relationship which can explain the great number of triggering in 1987
(Rickenmann & Zimmerman 1993). In spite of these numerous studies,
additional observations made from a wide sample of debris flows in other areas
of the Alps seem necessary in order to confirm or refute preliminary
predictions especially for places which have not been covered by glaciers recently.
The aim of
this paper is firstly to characterise the debris flow frequency since the beginning
of the 20^{th} century in 6 valleys located on the eastern part of the
Massif des Ecrins (French Alps); secondly to bring into evidence
geomorphological and climatic factors which control the frequency variations.
The concept of frequency in this article will be regarded on the one hand as
the number of cases established over a given period of time and on the other
hand as the number of events which occurred with a special length (3 events
with a travel distance of 300 m for example) over a given period of time (Van
Steijn, 1991, 1999).
For
this study debris flows were selected from a large surface area (28 km²) in the
northern part of the Massif des Ecrins (45°00’S, 6°30’E) (Figs. 12). In this
area 6 valleys not covered by glaciers since the Little Ice Age (according to
old documents and geomorphic observations) have been selected. These valleys consist of broad steep granite walls (100400m) overhanging
slope deposits which have already been studied (Jomelli & Francou 2000).
These deposits are situated between 1800m asl and 2400m asl which is close to
the 0°C annual isotherm.
At this
elevation more than 60% of the precipitations is snow, that is the reason why
the thickness of the snow cover frequently exceeds 3 meters. The data of
Monetier station (1490 m asl) which
is the closest to the selected sites show over the period 19612000 an annual
average temperature of 6°C and precipitation of 871 mm.




Figure 2. Example of a system composed of a rock face
and a slope deposit on which several debris flows occurred. Arrow = car for
scale. 
In the
area, the inventory and cartography of the debris flows were carried out using
the analysis of aerial photographs from 1952, 1960, 1967, 1971, 1974, 1981,
1986, 1989, 1994, 1996, 1999, and 2000 and field observations have been made
every year since 1995. The scale of these photographs was between 1: 15000 and
1: 30000. During the field work the
woody slopes were observed with special attention paid to compensate for the
difficulties in interpreting aerial photographs. Taking into account the
objectives, space scale selected in this study, and the particularity of this
surface area (national park, median and high slopes), debris flows were dated
by combining four approaches. Aerial photographs were combined with old
documents (Office National des Forêts,
Restauration des Terrains en Montagnes,
Archives départementales) and
dendrochronology (Shroder 1978, Strunk 1997, Blijenberg 1998) to date the
debris flows triggered between two aerial photographs. For debris flows older
than 1953 we added lichenometric measurements (Innes 1983, Mc Carroll 1994,
Helsen et al. 2002). These ones were performed as follow: we measured the
smallest diameter of the largest lichen on faces of blocks exposed to the
supposed trajectory of debris flows. One measure was done per block. These
measurements of Rhizocarpon sp. thalles were made on blocks with an
aaxis between 20 cm and 100 cm. Anomalous lichen shape were rejected to reduce
the risk of coalescence. The minimum size was fixed at 5 mm and the measures
were made with a precision of 1 mm. The chronological adjustment is based on a
growth curve made in the Massif des Ecrins (Jomelli 2002). The accuracy of
dates has been calculated with the procedure proposed by Mc Carroll (1994) and
gives confidence limits of ± 10 years.
In
dendrochronology, we worked from scars of Larix
decidua. To avoid taking into account the action of other processes like
the avalanches the selection of these scars was made with special attention by
taking into account their height and their position compared to the supposed
trajectory of the debris flow. Only
the scars on the trunk or the branches in the vicinity of the channel and/or
the levées on still living trees were taken into account in the analysis. The trunk or the branches have been divided
at the level of the scar, then polished in laboratory in accordance with the
classical methods of dendrogeomorphology (Strunk 1991). The counting of the
rings was carried out with a binocular magnifying glass.
Finally debris
flows which were impossible to date (31 and 18 for the years older than 1952)
were not taken into account in the analysis. For each dated debris flow, its
length was measured in the field and the altitude of the starting zone was
estimated from photographs analysis and field observations (accuracy ± 20m) (Le
Parcq 2000, Chochillon 2002).
To analyse the debris flows
frequency the method has relied on working from a system including the rock
face and its slope deposit on which one or several debris flows have been
triggered (Fig. 2). This system is under the influence of a geomorphological context
(length of the rock face, elevation) and climatical conditions. These
conditions play a role on two times scales: a short time which commands the
debris flows triggering and a long time which controls the production of the
stock of debris which will be mobilized during the event. So two statistical
modelling have been made. To make a model of the effects of these two types of
variables a logistic regression (Aldrich & Nelson 1984) was used. Logistic
regression analysis is often used to investigate the relationship between
discrete response like event/nonevent and a set of explanatory variables. The
dependent variable Y_{i} is
ordered and has values from 1 to k. The model based on cumulative probabilities
is :
_{}+ e (1)
in which p_{i} = f (x) is the logistic distribution function, where i varying from 1 to k, with the intercept a_{i} varying from a_{1} toa_{k1} and b’ is the slope coefficient and e the error. The logistic distribution constrains the estimated probabilities to lie between 0 and 1. The cumulated probability p_{i} of the frequency i is calculated from the following equation.
(2)
The
analysis of variations in debris flows frequency is based on 142 events which
have occurred since 1900 in part of the Massif des Ecrins (Fig. 3). The detail
of the number of debris flows started by small valley is given in Table 1. In
Figure 3 one can also observe a strong spatial or temporal variability in the number of debris flows without being
able to observe a significant tendency.
To take into account the temporal resolution variable according to
methods (annual for dendrochronology and pluriannual for lichenometry), data
have been grouped by periods of 20 years. This time period corresponds to the
highest error estimation of dating methods. At first sight, two distinct stages
appear: a first stage (19001959) during which the number of events increases
and is followed by a second stage (19602000) during which the number
decreases. In fact, these two periods are not strictly comparable because
during the first one the inventory of events cannot be considered as complete.
Indeed, Van Steijn (1999) said, “In a system with a high degree of activity,
younger deposits will easily cover or sometimes erode the older flows.”
Period 
19001919 
19201939 
19401959 
19601979 
19802000 

Valley 
T 
L 
D 
T 
L 
D 
T 
L 
D 
T 
L 
D 
T 
L 
D 
1 
0 
0 
0 
6 
3 
1 
10 
6 
2 
4 
0 
3 
2 
0 
0 
2 
2 
2 
0 
8 
7 
0 
8 
3 
1 
5 
0 
2 
3 
0 
0 
3 
2 
2 
1 
6 
6 
0 
4 
0 
4 
7 
0 
4 
4 
0 
4 
4 
1 
1 
0 
7 
5 
2 
5 
1 
2 
7 
0 
0 
3 
0 
0 
5 
4 
3 
1 
3 
3 
0 
9 
0 
3 
4 
0 
0 
4 
0 
1 
6 
3 
3 
0 
5 
5 
0 
7 
3 
0 
8 
8 
0 
1 
1 
0 
To estimate
this rate of covering or erosion over the 19001959 period, we have calculated
the rate of debris flows recovered or eroded since 1953 from aerial
photographs. It is 13% for 50 years. By analogy, we could say that the number
of debris flows between 1900 and 1950 shown in Figure 3 is underestimated by
13% on the assumption that climatic conditions are almost comparable over the
two periods and that the number of systems recording
several triggerings is almost the same over the two periods. Over the 20^{th}
century observations realized from climatic homogenised data series
in the Alps show decadal fluctuations which can be sometimes significant (Böhm
et al. 2001). Over the period 19002000 just one triggering was observed for
only 19% of systems. Out of this percentage 2% occurred
during the second half of the 20^{th }century. As for the systems with
several triggerings 54% occurred during the first half of the 20^{th}
century and 57% since 1980. Consequently, the real rate of covering or erosion over the 19001959
period is difficult to estimate.
Over the
second period the inventory can be considered as representative of the real
debris flow frequency in the valleys. The number of debris flows decreases
between 19601980 and 19802000. But this decrease is not significant
(KruskalWallis test at 0.05 level).
We have
studied the evolution of debris flows frequency according to their track
length. Figure 4 shows important variations in the debris flow frequency. If we
consider debris flows whose lengths exceed 300 m, it seems that there has not
been a clear change in the frequency over the whole period even if doubts
remain concerning the number of events over the 19001950 period (Tab. 2).
For smaller sized debris flows i.e smaller
than 300 m if the increase in frequency between 1900 and 1950 may be discussed
considering problems linked to sampling, a significant decrease in the number
of debris flow has been observed
between 1960 and 2000 when analyzing the data over twentyyear periods (Tab.2). If one considers the mean return
period (time between 2 debris flows triggered in the same system) of the debris
flows with lengths smaller than 400m in each valley, it decreased from 36 years
for 19601980 to 15 years for 19802000. In others words the number of years
for which one or several triggering have been observed between 19601980 and
19802000 has increased significantly (Sign test in Table 2). This return
period knows a great spatial variability, some slope deposits are affected by
only one event whereas other slope deposits are eroded by 3 and sometimes 4 debris flows.
Test 
<100m 
100199m 
200299m 
300399m 
400499m 
500599m 
600699m 
700799m 
>800m 
KS 
1 
0.01 
0.04 
0.07 
0.33 
1 
0.18 
1 
1 
Sign 
1 
0.01 
0.01 
0.034 
1 
1 
0.625 
1 
0.5 
We
have tried to point out different factors explaining this variability
emphasised before. Two logistic models were tested. The first one aimed at
explaining the frequency variability by geomorphological parameters. The second
one aimed at explaining the variability according to climatic parameters.
To
determine an frequency probability according to geomorphological parameters, we
used an ordinal logistic regression over the 19532000 period, for which
inventory can be seen like complete. A total of 76 debris flows were selected
and coded as follows: 4 for systems without triggering since 1953, and 3, 2, 1
for systems with one, two and more than two events respectively. The
independent variables tested were the altitude of the triggering zone, Am (in m), the rock face surface, S (in ha), the rock face inclination
(degrees), its height (m) and the exposition. These variables
have been calculated from a topographic map (scale 1: 25000).
The
independent variables which give the better fit are the surface of the rock
face (S in ha) and the altitude of
the triggering zone (Am in m).
The model
is :
Logit(p_{i})
= α_{i} + (0.00248 x Am) + (0.0993 x S) + e (3)
with
constant terms a_{i} is 5.3760 for p_{0}, 8.0336 for p_{1},
and 9.6430 for p_{2}.
(number of debris flows analysed = 76).
The
coefficients of the model are estimated by maximum likelihood estimation. One
method of model evaluation is to consider the likelihoodratio statistic. This
statistic tests the hypothesis that all coefficients except the constant are 0.
For one variable, the wald statistic tests the explanatory variable effect is
significant. The overall model is statistically significant (Tab. 3). The estimates are highly significant (Tab. 4), the percentage of correct predictions is
74.7% and the discriminant factor c = 0.781.
In Figure 5, the higher the elevation and the larger the
surface, the higher is the predicted probability. Logically this probability
decreases to the threshold of the number of triggerings considered in this
study i.e. at least one, two or three triggerings. Thus for a 20ha rock face at
an altitude of 2000 m the predicted probability is about 0.83, 0.25 and 0.06 of
observing at least one (Fig. 5c), two (Fig. 5b), and three (Fig. 5a)
triggerings, respectively.
Tests 
ChiSquare 
Degree of freedom 
Pr>ChiSq 
Likelihood
Ratio 
18.9931 
2 
<.0001 
Wald 
16.789 
2 
0.0002 
Parameter 
Degree of freedom 
Estimate 
Standard
error 
Chisquare 
Pr>chiSq 
Intercept 
1 
5.3760 
1.8745 
8.2253 
0.0041 
Intercept 2 
1 
8.0336 
2.0254 
15.7332 
<.0001 
Intercept 3 
1 
9.643 
2.1104 
20.8776 
<.0001 
Am 
1 
0.00248 
0.000895 
7.6734 
0.0056 
S 
1 
0.0993 
0.0308 
10.4203 
0.0012 
In the
second model, we have tried to determine the effect of climatic conditions on
the debris flow triggering. From a theoretical point of view, we observe a
triggering when two conditions are met: 1) a water flood which carries
materials; 2) a stock of available debris (Pech & Jomelli 2001). The water
flood has been estimated from climatic observations made since 1961 at the
station of MonetierlesBains (1490 m asl) which is the closest to the selected
sites. We have tested mean annual precipitation during the year of the
triggering, seasonal amount of precipitation which occur during spring, summer,
autumn or winter. Finally we have added the number of days between June 15^{th
}and October 15^{th }during which rainy events were greater than
20 mm and 30 mm/day.
We assume
that the available material depends on temperatures (see below). The
independent variables tested were the mean
annual temperature of the year of triggering, the mean temperature of
spring, summer, autumn and winter, the minimal temperature during winter or
spring and the total number of freezing days per year since the last event.
The analysis is based on 39 debris
flows annually dated whose date of the first triggering was after 1961, thus
allowing the number of freezing days since the last event to be calculated. The
binary logistic regression has been made yearly, giving to years without a
triggering the code 0 and the code 1 to years with a triggering.
The
independent variables which give the best fit are the cumulated number of
freezing days since the last event (Nfr
in thousand) and the number of daily rainfall greater than 30 mm/day (Nd).
The model
is :
Logit(p_{1}) = 4.7236_{ } (0.388 x Nfr)  (0.5717 x Nd) +
e (4)
(number of debris flows = 39)
The
model has a good fit quality. The model is globally statistically significant
(Tab. 5). The estimates are
highly significant (Tab. 6) and the percentage of correct predictions is
85.1% and the discriminant factor c = 0.82.
Test 
ChiSquare 
Degree of freedom 
Pr>ChiSq 
Likelihood
Ratio 
28.8788 
2 
<.0001 
Wald 
26.7849 
2 
<.0001 
Parameter 
Degree
of freedom 
Estimate 
Standard
error 
Chi
Square 
Pr>chiSq 
Intercept 
1 
4.7236 
0.5129 
84.8124 
<.0001 
Nd 
1 
0.5717 
0.1510 
14.328 
0.0002 
Nfr 
1 
0.388 
0.
1241 
9.7719 
0.0018 
Figure 6 shows the probability of triggering according to the cumulated
number of freezing days since the last
triggering for 1, 2, 3, 4 and 5 days between June 15^{th }and
October 15^{th }during which precipitations were greater than 30
mm/day. We notice that the more the freezing days are since the last event the
more the probability of observing a new triggering increases. It has also been
observed that this probability increases according to the rise of the number of
rainy days above 30 mm/day. For example, for 6000 freezing days since the last
event, the probability of a debris flow triggering is 0.25 for a year during
which 2 days present precipitations above 30 mm; it is 0.6 for a year during which 5 days present precipitations above
30 mm.
Figure 6. Probability values according to the cumulated number of freezing days (Nfr) since the last triggering for i days (Ri), between June 15th and October 15th during which rain is greater than 30 mm/day.
The statistic analysis of debrisflow inventory in the Massif des Ecrins
permits one to discuss the role of the different climatic parameters in
debrisflow triggering. Until now researchers have largely insisted on the role
of intense precipitations, even if debris flows can also be triggered by a
sudden release of water stored under a glacier, by the breaching of a morainic
dam (Evans & Clague 1994) or by melting snow. Many authors (Caine 1980, Nyberg
& Rapp 1998, Van Steijn et al.
1988, Blijenberg 1998) have established debris flow triggering thresholds in
relation with some precipitation intensities. Some results even show that
several minutes during which the intensity is really greater than the one
calculated to the hourly length can be sufficient to cause a triggering. Our
frequency model obtained from climatic data confirms the preponderant role of
precipitation. In this model, precipitation data are
calculated daily, whereas most studies mention precipitation data which are
calculated hourly. Moreover, our climatic data have been collected at a low
elevation station. However
the probability analysis permits one to take into account these uncertainties
concerning rainfalls. For this study, it seems
that the threshold of 20 mm/day has not been relevant compared with 30 mm/day.
The role of the number of freezing days, which appears clearly in equation 4, is however less frequently mentioned in the literature. Taking this parameter into account permits one to estimate the amount of debris to be mobilized, which is the second variable playing a role in the debrisflow triggering. The formation of a stock of debris resulting from a recent glacial retreat has been already shown by Haeberli et al. (1990) and by Zimmermann & Haeberli (1992). In our study this production of debris is mainly due to frost action. This mechanism linked to water freezing inside the rock is complex in detail. Of course the amount of debris produced by frost action does not depend only on the number of freezing/thawing cycles for a specific lithology. Other factors play a role, notably the duration and the intensity of frost combined with the water saturation rate of the rock (Coutard & Francou 1989, Matsuoka et al. 1997). Moreover, the number of freezing days determined at low altitude and defined by air temperature is, of course, not strictly comparable to the freeze of rock face at high altitude. Unfortunately, these parameters are rarely available for an analysis made over such a period and at this regional scale. This is the reason why the probability model which permits one to take into account these uncertainties has been chosen. On the other hand, the cumulated number of freezing days since the last event allows to understand that debris flows do not occur independently of each other in a system. Once such a flow has occurred in a particular place, then another cannot occur until there is sufficient debris.
However,
the quantity of rocky debris resulting from frost action likely to accumulate
at the bottom of the rock face depends, for a specific lithology, also on the
size of the rock face. The larger the face is, the more voluminous the quantity
of debris will be and the higher the frequency of a debris flow. This is the
reason why the debris flow frequency in Equation 3 is strongly linked to the
surface of the rock face. Of course, the amount of
debris will become more important as the altitude of the rock face will be
high, thus allowing a bigger number of freezing/thawing cycles and a bigger
intensity. The
geomorphological model shows that systems, which have not recorded debris flows
triggering since 1952, are most of the time situated at a low altitude and present
a low rock face.
For all
things considered, if we could admit a link between the debris flow frequency
and climatic parameters, which in turn have known fluctuations in this sector
for the previous years (Thevenon 1999, Bocquet 2001), as observed in the other
Alpine regions (Beniston 1994, Beniston et
al. 1997, Böhm et al. 2001), we might expect a certain modification in
the rhythm of the triggering of this process for some years to come.
This study was based on 142 debris flows triggered since the beginning
of the 20^{th} century in the Massif des Ecrins. The triggering of such
debris flows is independent of the current glacial retreat. The results show
that it is difficult to compare the two periods of 19001950 and 19502000 because
the number of debris flows over the first half of the century has been probably
underestimated. During this last period we have observed a decrease in the
debris flow frequency for debrisflow lengths between 200 and 399 m. Finally,
the results of the two statistical models show that the frequency depends first
on geomorphological variables, such as the rock face size and its altitude. The
second model shows that the frequency depends on climatic variables. It
confirms the preponderant role of rainfall but also brings to light the role of
the cumulated number of freezing days between two events which play a role in
the formation of a stock of debris which can be mobilized.
Acknowledgements
We would like to extend our thanks to K. Meitz and three anonymous
reviewers for their constructive remarks on an earlier version of this paper.
This research was carried out as part of the APN and Eclipse of the National
Scientific Research Centre and the IMFREX programme of the Ministry of Research.
Special thanks are due to C. Delamare (MeteoFrance), to the scientist chief of
the Parc National des Ecrins, to G. Rovera for giving us meteorological data,
to L. Dumoulin for checking format instructions, and also to R. Greenstein for
reviewing an English version of this paper.
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