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, Meudon-bellevue, France

C. Chochillon & P. Pech

Université Paris 1 Panthéon-Sorbonne, 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 20th 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 1900-1950 and 1950-2000 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 200-399 m class lengths. We have also observed a decrease in the number of debris flows between 1950-1975 and 1975-2000. 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.


1        introduction

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 19th 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 20th 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).

2        Study Area

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. 1-2). 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 (100-400m) 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 1961-2000 an annual average temperature of 6°C and precipitation of 871 mm.

 


Adobe Systems

Figure 1. Location map.

 

 

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.

 

3        Methods

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 a-axis 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/non-event and a set of explanatory variables. The dependent variable Yi is ordered and has values from 1 to k. The model based on cumulative probabilities is :

+ e                                                                    (1)

in which pi = f (x) is the logistic distribution function, where i varying from 1 to k, with the intercept ai varying from a1 toak-1 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 pi of the frequency i is calculated from the following equation.

                                                                                                                 (2)

4        Result

4.1       Debris flows frequency analysis since 1900

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 pluri-annual 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 (1900-1959) during which the number of events increases and is followed by a second stage (1960-2000) 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.”

 

Table 1.  Number of debris flows in the 6 valleys studied by type of datation, lichenometry (L), dendrochronology (D) and the total of the four methods (T).

 

Period

1900-1919

1920-1939

1940-1959

1960-1979

1980-2000

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


 


Figure 3. Frequency of debris-flow triggerings since 1900 in 6 valleys.

 

 

To estimate this rate of covering or erosion over the 1900-1959 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 20th 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 1900-2000 just one triggering was observed for only 19% of systems. Out of this percentage 2% occurred during the second half of the 20th century. As for the systems with several triggerings 54% occurred during the first half of the 20th century and 57% since 1980. Consequently, the real rate of covering or erosion over the 1900-1959 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 1960-1980 and 1980-2000. But this decrease is not significant (Kruskal-Wallis 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 1900-1950 period (Tab. 2).

 

Figure 4. Frequency of debris flows according to their track length.

 

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  twenty-year 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 1960-1980 to 15 years for 1980-2000. In others words the number of years for which one or several triggering have been observed between 1960-1980 and 1980-2000 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.

 

 

Table 2. Kolmogorov-Smirnov (K-S) and Sign probability values for debris flows frequency over  the 1960-1980 and 1980-2000 periods.

 

Test

<100m

100-199m

200-299m

300-399m

400-499m

500-599m

600-699m

700-799m

>800m

K-S

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

 

4.2       Statistic modelling

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 1953-2000 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(pi) = αi + (0.00248 x Am) + (0.0993 x S) + e                                                                    (3)

with constant terms ai is -5.3760 for p0, -8.0336 for p1, and -9.6430 for p2. (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 likelihood-ratio 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.

 

Adobe Systems

Figure 5. Predicted probabilities of  debris flows (pi) according to the elevation (Am) and the surface of the rock face (S) for at least one event (c), two events (b), and three events (a).

 

Table 3. Tests of maximum likelihood estimation for the geomorphic model.

 

 

Tests

Chi-Square

Degree of freedom

Pr>ChiSq

Likelihood Ratio

18.9931

2

<.0001

Wald

16.789

2

0.0002

 

 

Table 4. Analysis of maximum likelihood estimates for the geomorphic model.

 

Parameter

Degree of freedom

Estimate

Standard error

Chi-square

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 Monetier-les-Bains (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 15th and October 15th 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(p1) = 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.

 

 

Table 5. Tests of maximum likelihood estimation for the climatic model.

 

Test

Chi-Square

Degree of freedom

Pr>ChiSq

Likelihood Ratio

28.8788

2

<.0001

Wald

26.7849

2

<.0001

 

 

Table 6. Analysis of maximum likelihood estimates for the climatic model.

 

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 15th and October 15th 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.

 

Adobe Systems

 


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.

5        Discussion

The statistic analysis of debris-flow inventory in the Massif des Ecrins permits one to discuss the role of the different climatic parameters in debris-flow 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 debris-flow 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.

6        Conclusion

This study was based on 142 debris flows triggered since the beginning of the 20th 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 1900-1950 and 1950-2000 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 debris-flow 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 (Meteo-France), 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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