Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands

GEOMOR-04122; No of Pages 9 Geomorphology xxx (2012) xxx–xxx

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Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands Mads-Peter J. Dahl a, b, c,⁎, Lis E. Mortensen b, Niels H. Jensen c, Anita Veihe c a b c

Norwegian Water Resources and Energy Directorate, Middelthunsgate 29, Postbox 5091 Majorstua, 0301 Oslo, Norway Jarðfeingi (Faroese Earth and Energy Directorate), Brekkutún 1, Postbox 3059, FO-0110 Tórshavn, The Faroe Islands Department of Environmental, Social and Spatial Change, Roskilde University, Universitetsvej 1, Postbox 260, DK-4000 Roskilde, Denmark

a r t i c l e

i n f o

Article history: Received 8 June 2011 Received in revised form 22 June 2012 Accepted 25 September 2012 Available online xxxx Keywords: Debris-slides Flow-type landslides The Faroe Islands Aerial photograph interpretation Magnitude–frequency analysis Discriminant function analysis

a b s t r a c t The Faroe Islands in the North Atlantic Ocean are highly susceptible to debris-avalanches and debris-flows originating from debris-slide activity in shallow colluvial soils. To provide data for hazard and risk assessment of debris-avalanches and debris-flows, this study aims at quantifying the magnitude and frequency of their debris-slide origins as well as identifying which preparatory factors are responsible for the spatial debris-slide distribution in the landscape. For that purpose a debris-slide inventory was generated from aerial photo interpretation (API), fieldwork and anecdotal sources, covering a 159 km2 study area in the northern Faroe Islands. A magnitude– cumulative frequency (MCF) curve was derived to predict magnitude dependant debris-slide frequencies, while preparatory factors responsible for spatial debris-slide distribution were quantified through GIS-supported discriminant function analysis (DFA). Nine factors containing geological (lithology, dip), geomorphological (slope angle, altitude, aspect, plan and profile curvature) and land use (infield/outfield, sheep density) information were included in the multivariate analysis. Debris-slides larger than 100 m2 with magnitude expressed as topographic scar area can be predicted from the power–law function: Y=936.26X−1.277, r2 =0.98 while a physical explanation is preferred for the roll-over pattern of smaller slope failures. The DFA is able to correctly classify app. 70% of the modeled terrain units into their pre-determined stable/unstable groups. Preparatory factors responsible for the spatial debris-slide distribution are aspect, slope angle, sheep density, plan curvature and altitude, while influence of the remaining factors is negligible. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The Faroe Islands in the North Atlantic Ocean are highly susceptible to rainfall-induced landslides. Steep mountains rising to a height of app. 900 m above sea level and high precipitation (900–3200 mm/year) (Cappelen and Laursen, 1998) favor the initiation of shallow translational debris-slides in thin colluvial soil covering basaltic parent material. With remolding of the runout material, debris-slides quickly develop into extremely rapid debris-avalanches and debris-flows, as defined by Hungr et al. (2001). As debris-avalanches and debris-flows approach valley bottoms, they constitute a threat to human lives and interests in the Faroese society, since buildings and infrastructure are generally located here. Following several landslide incidents in recent years, partially described in Christiansen et al. (2007), a research project has been initiated at Jarðfeingi (Faroese Earth and Energy Directorate) to assess landslide risk in the Faroe Islands. A central element in landslide risk assessment is evaluating the landslide hazard, in which landslide location, volume and frequency ⁎ Corresponding author. Tel.: +47 94531780. E-mail addresses: [email protected], [email protected] (M.-P.J. Dahl), [email protected] (L.E. Mortensen), [email protected] (N.H. Jensen), [email protected] (A. Veihe).

are important elements (Fell et al., 2005, among others). An initial model to predict spatial debris-avalanche occurrence in the Faroe Islands was developed by Dahl et al. (2010). However, the model mainly focused on delineating runout areas and only few assumptions were made in the prediction of initiation zones. Thus, in the process of further assessing the hazard from debris-avalanches and debris-flows, this study aims to quantify the magnitude and frequency of their debris-slide origins as well as identifying which preparatory factors are responsible for spatial debris-slide distribution in the landscape. Temporal landslide occurrence can be predicted from either potential slope failure analysis or statistical treatment of past landslide events (Picarelli et al., 2005; Corominas and Moya, 2008). In the latter category, a well known methodology applied in this study is magnitude– frequency analysis. In magnitude–frequency analysis, complete and sometimes multi-temporal landslide inventories are derived from aerial photo interpretation (API), fieldwork, and/or other available information (Hovius et al., 2000; Dai and Lee, 2001; Brardinoni and Church, 2004; Guthrie and Evans, 2004; Hungr et al., 2008). Statistical relationships such as power–law scaling or more complex distributions are then applied to predict magnitude dependant landslide frequencies (Stark and Hovius, 2001; Guzzetti et al., 2002; Malamud et al., 2004).

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Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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The application of magnitude–frequency analysis in this study was chosen as a consequence of several unique characteristics in the Faroese geographical setting. Vegetation is dominated by low grasses and herbs, while trees are virtually absent. The low vegetation clearly demarcates debris-slide scars, which are thus easily identified from API. Absence of trees diminishes the bias from nonregistered events hidden under forest canopy; an issue addressed in other studies (Brardinoni et al., 2003; Brardinoni and Church, 2004; Miller and Burnett, 2007; Turner et al., 2010). Moreover, a cool temperate climate (cf. Section 2) slows down vegetational processes including overgrowth of debris-slide scars, which thus remain visible and unchanged in the landscape for many years. Preparatory factors responsible for spatial debris-slide distribution in the study area were identified through discriminant function analysis (DFA). DFA and other multivariate statistical methods are commonly used in landslide literature to identify the preparatory factors contributing to slope instability at the regional scale (Baeza and Corominas, 2001; Dai and Lee, 2002; Santacana et al., 2003; Ayalew and Yamagishi, 2005; Duman et al., 2006; Guzzetti et al., 2006; Carrara et al., 2008; Van Den Eeckhaut et al., 2009). Compared to qualitative methods like landslide inventory mapping or expert evaluation (Malgot and Mahr, 1979; Ives and Messerli, 1981; Rupke et al., 1988; Wachal and Hudak, 2000; Morton et al., 2003; Sarkar and Anbalagan, 2008), an important advantage of using statistical approaches to analyze spatial landslide occurrence is that the latter allow quantitative and more objective investigations of factors potentially contributing to slope instability. 2. Regional setting Debris-slide registration was carried out in a 159 km 2 study area, located on the three islands Borðoy, Kunoy and Kalsoy in the northern Faroe Islands (Fig. 1). Numerous settlements are located in the area including Klaksvík, which is the second largest town in the Faroe Islands with app. 4700 inhabitants. Urban areas and infrastructure

are located in valleys at the foot of steep slopes, making them susceptible to landslides of various types including debris-avalanches and debris-flows. The three islands as well as the entire archipelago are remnants of an early Palaeogene basalt plateau related to the opening of the NE Atlantic Ocean (Rasmussen and Noe-Nygaard, 1969). The plateau mainly consists of three tholeiitic basalt formations; the lower Beinisvørð Formation, the middle Malinstindur Formation and the upper Enni Formation (Passey and Jolley, 2009) of which the latter two are represented in the study area (Fig. 2). The Malinstindur Formation consists of plagioclase-phyric lava flows with a thickness from b1 m to app. 10 m, while the Enni Formation mainly consists of aphyric, crypto phyric and olivine-phyric lava flows with a thickness from app. 8 m to 11 m (Rasmussen and Noe-Nygaard, 1969). The two basalt formations in the study area dip app. 1.4° towards east, and interbasaltic tuff-layers with thicknesses of b1 to 4 m are mainly found between the lava flows in the Enni Formation (Rasmussen and Noe-Nygaard, 1969). Water and wind erosion, together with weathering and Quaternary glacial erosion, has sculptured the original basalt plateau and created the present landscape (Humlum, 1996; Christiansen, 1998) with U-shaped valleys and high mountains rising from the ocean to >800 m above sea level (Fig. 2). Moving upwards from the sea, concave slopes become steeper with altitude until reaching linear rocky outcrops, which are somewhere succeeded by low relief landscapes or upper convexities and flat mountain tops. Formation of Quaternary colluvial soils (Christiansen et al., 2007; Dahl, 2007; Veihe and Thers, 2007) covering the basaltic parent material exhibit depths up to 5 m in the study area. Grasses and herbs, which comprise the only vegetation covering the area, are grazed by sheep throughout the year. The climate at sea level is temperate oceanic, humid and windy with mild winters and cool summers. Annual precipitation is app. 2700 mm (Cappelen and Laursen, 1998). While the mean annual air temperature (MAAT) at sea level is 6.5 °C (Cappelen and Laursen, 1998), a mean annual lapse rate of − 0.0077 °C/m (Christiansen and

Fig. 1. Overview of the Faroe Islands and the study area.

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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the basaltic parent material (Fig. 3). Slope movement is thought to be initiated by either reduction in apparent cohesion within the soil or by buildup of positive pore water pressures at potential slip surfaces. Most slip surfaces are located at the soil/rock boundary (Fig. 3A) and measured debris-slide volumes vary from 16 m3 to 14 216 m 3 (Dahl et al., 2010). Debris-slides can either occur as new slope movements or as retrogressive failures from existing landslide scars and are widespread over most of the study area. With remolding (i.e. extensive internal deformation) of the runout material, debris-slides quickly develop into debris-avalanches and debris-flows, rapidly propagating down the slopes and often reaching valley bottoms (Fig. 3B and C). Debris-avalanches generally maintain their initial volumes, while debris-flows can increase in volume by erosion of bed material along their confined runout path.

4. Methodology 4.1. Debris-slide registration

Fig. 2. Lithology and elevation map of the study area.

Mortensen, 2002) indicates a MAAT of 0.1 to 0.3 °C at the highest points within the study area. 3. Landslide characteristics Of the various landslide types found in the study area, this paper focuses on translational debris-slides which, when applying the landslide velocity scale of Cruden and Varnes (1996), develop into very rapid to extremely rapid debris-avalanches and debris-flows, as defined by Hungr et al. (2001). The debris-slides, which are triggered by rainfall and snowmelt, occur in the shallow colluvial soil covering

For the analysis, API was used for generating a landslide inventory containing 219 debris-slides over the 51 year period 1958–2009. Initial identification was done using two aerial photograph series from 1958 and 2002/2004, on which debris-slides were well detectable. It was found that recent debris-slide events prior to 1958 were still visible on the 2002/2004 photographs. Subsequently, an aerial photograph series from 2009 was used to detect debris-slides which had occurred later than 2002/2004. Debris-slides were identified as either new slope movements or as retrogressive failures from existing landslide scars. It was noted down whether the events had transformed into debris-avalanches or debris-flows. Debris-slides on analogue photographs were identified by use of a 10 x magnifying glass. Excluded from the API registration were slope failures related to ongoing coastal erosion as well as patterns of small debris-slide-like features occurring in non-vegetated high-altitude areas. The latter were assumed to be more related to aeolian and wash transport processes. To support the API registration, 30% of the identified debris-slides were verified through fieldwork, local photographs, eyewitness accounts and newspaper articles of the events. Photographs and eyewitness accounts were collected from a large number of interviews with local people and employees at the Faroese Office of Public Works. Newspaper

Fig. 3. (A) Debris-slide scar with arrows marking the slip surface located at the soil/rock boundary. (B) Debris-avalanche originating from a debris-slide. (C) Debris-flow originating from a debris-slide.

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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articles of the events were found by searching through microfilms at the National Faroese Library. 4.2. Magnitude–frequency analysis To analyze debris-slide frequency related to magnitude, a magnitude– cumulative frequency (MCF) curve was derived. For that purpose debris-slide events nd were ranked in order of decreasing magnitude, with magnitude expressed as topographic (i.e. inclined) debris scar area SA, and the frequency fi of an individual debris-slide of rank i determined as fi ¼

1 T

nd X

Gj ¼ C 1 X 1j þ C 2 X 2j þ ⋅⋅⋅ þ C p X pj

ð4Þ

 as the centroid of group j (j = α,b for the two presence/absence with G j groups). As a consequence of the presence/absence groups having unequal n, the threshold DS value GT for classifying samples into the two groups is calculated as (Dillon and Goldstein, 1984):

ð1Þ

with T as the registration period (51 years). Data for the MCF curve was obtained by adding up the calculated frequencies using the equation Fi ¼

Quinn and Keough, 2002). Multiplying all values of C with their associated scores of X for the entire dataset and adding a constant A gives a mean DS value of zero (Tabachnick and Fidell, 2001). Values of DS which represent centroids of the presence/absence groups are calculated as

ð2Þ

fi

i¼1

with Fi as the annual debris-slide frequency of some minimum debris-slide scar area, SA. Finally, a power–law model was fitted to predict magnitude dependent debris-slide frequencies within the study area. 4.3. Discriminant function analysis 4.3.1. Basic modeling terms DFA is a multivariate statistical method, developed by Fisher (1936) to classify samples into a number of pre-determined groups from a range of measurements for each sample (Quinn and Keough, 2002). In this study, the pre-determined groups chosen are the presence/absence of debris-slides within a defined slope unit of the landscape represented by GIS-derived raster grid cells, cf. Sections 4.3.3. The samples to be classified are a number of grid cells specifically chosen for the analysis, where debris-slides are either present or absent. Measurements in each sample are of a geological, geomorphological or land-use character and represent the preparatory factors which are being tested for potential contribution to slope instability. Sample classification was done by finding a linear combination of measurements that maximizes the probability that samples belong to their pre-determined “debris-slide presence/absence” group (Quinn and Keough, 2002). The linear combination called the discriminant function can be written as DS ¼ A þ C 1 X 1 þ C 2 X 2 þ ⋅⋅⋅ þ C p X p

ð3Þ

where DS is the discriminant score for classifying each sample, X represent each p measurements, and C are discriminant function coefficients for each X that maximize the proportion of betweengroups to within-groups variance (Baeza and Corominas, 2001;

GT ¼

nb Ga þ na Gb na þ nb

ð5Þ

An efficient discriminant function should be able to correctly sort samples into their pre-determined groups with minimal error. Discriminant function coefficients which are standardized by within-group variances (SDFCs) hold information about the contribution of each factor to the discrimination of groups; this can be interpreted as their contribution to slope instability. Increasing positive coefficient values reflect larger contribution to slope instability, while increasing negative coefficient values reflect larger contribution to slope stability. 4.3.2. Preparatory factors Information on nine geological, geomorphological and land-use factors (Table 1) was collected within the study area and tested for their contribution to spatial debris-slide distribution by use of the DFA: 4.3.2.1. Slope angle. Slope angle has been shown to be a key factor when assessing shallow landslide distribution, both in the Faroe Islands (Dahl et al., 2010) and in other studies (Baeza and Corominas, 2001; Dai and Lee, 2002; Zêzere et al., 2004). Larger landslide frequency with increase in slope angle results from increasing driving forces at the potential slip surface. Thus slope angle was considered a relevant preparatory factor for the statistical analysis. 4.3.2.2. Aspect. Slope aspect was included in the statistical analysis, since it has shown to influence spatial landslide distribution (Crozier et al., 1980; Lan et al., 2004). Variations in slope stability with changes in aspect can for instance be due to changes in soil moisture content on sunny vs. shaded slopes (Sidle and Ochiai, 2006). To analyze the contribution of aspect, the preparatory factor was separated into two north-to-south and east-to-west variables containing data on aspect in 10° intervals. For example, in the north-south variable (ASPECT NS), angle intervals 350–0° and 0–10° was denoted 5°, angle intervals 340–350° and 10–20° was denoted 15° and so on.

Table 1 Overview of preparatory factors and resulting variables for use in DFA. Preparatory factor

Variable for DFA

Description of variable

Data type (value range)

Slope angle Aspect

SLOPE ASPECT NS ASPECT EW Sqr ALTITUDE LITHOLOGY LITHO DIP PLAN CURVE PROF CURVE SDI LAND FIELD

Slope angle Slope aspect north to south in 10° intervals Slope aspect east to west in 10° intervals Height above sea level Presence of Malinstindur or Enni Formation Inward, along or outward dip Convergent to divergent slope Convex to concave slope Sheep density Presence of infield or outfield area

Continuous (0 – 88°) Continuous (0–180°) Continuous (0–180°) Continuous (−3 to 829 m) Binary (0/1) Continuous (dummy) (−1 to 1) Continuous (−27 to 23*) Continuous (−20 to 20*) Continuous (0–90 sheep/km2) Binary (0/1)

Altitude Lithology Dip Plan curvature Profile curvature Sheep density Infield/outfield

*Unit for curvature: 100−1 z-units, i.e. height units in the DEM (ESRI ArcMap 9.3).

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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4.3.2.3. Altitude. Aune and Førland (1986) indicated that precipitation in the Faroe Islands may increase by 34% per 100 m above sea level. The increase in precipitation may cause landslide occurrence to increase with altitude, which is seen in Dai et al. (2001). Since altitude was considered a reasonable proxy variable for precipitation, the parameter was included in the DFA. 4.3.2.4. Lithology. Several studies have shown that variations in lithology can play a key role in spatial distribution of shallow landslides (Avanzi et al., 2004; Wakatsuki et al., 2005; Matsushi et al., 2006). Since the parent materials, Malinstindur and Enni Formations, in the study area have different characteristics in terms of flow layers and presence of interbasaltic tuff-layers (cf. Section 2), lithology was considered a relevant preparatory factor. 4.3.2.5. Dip. The dip angle of lithological layers has shown to influence landslide occurrence (Clerici et al., 2002; Avanzi et al., 2004), and was therefore considered relevant for the DFA. Point data on dip direction and angles, which were quite constant within the study area were used for setting an average fixed dip angle of the lithological layers. Subsequently, four 90° categories around the compass were constructed to determine where the dip was inward, outward or along the slope. 4.3.2.6. Plan and profile curvature. Sidle and Ochiai (2006) argued that since subsurface water is more easily concentrated on convex and convergent hillslopes, these are more susceptible to landslides than divergent and planar slopes. This was confirmed by Gao (1993) who found a high susceptibility to translational landslides on convergent slopes compared to other slope types. In addition, Avanzi et al. (2004) found shallow landslides to be most abundant in hollows, followed by planar slopes and ridges. Thus, plan and profile curvatures were considered relevant preparatory factors for the statistical analysis. 4.3.2.7. Sheep density. As described earlier, the study area is grazed by sheep throughout the year. Results from papers quantifying the effect from grazing on root development are ambiguous (Löffler, 2000; Damhoureyeh and Hartnett, 2002; Pucheta et al., 2004), and no such data exist for the Faroe Islands. However, Fosaa and Olsen (2007) showed that vegetation height and ground cover were reduced by sheep grazing in the Faroe Islands. Grazing is also believed to generally increase soil erosion in the Nordic Countries (Nordic Council of Ministers, 2007). Moreover, indications of increasing shallow landslide occurrence from cattle and sheep grazing have been observed by Meusburger and Alewell (2008). Thus, the density of sheep as a proxy for grazing intensity within the study area was considered an important factor to be included in the DFA. 4.3.2.8. Infield/outfield. The study area is divided into infield and outfield land-use areas (Thorsteinsson, 2001, 2007). Infield areas are inhabited and covered by buildings and roads or used for gardening, growing hay and different vegetables. Outfield areas are uninhabited, uncultivated areas mainly used for sheep grazing. The difference in land use was considered a relevant preparatory factor for the statistical analysis. Information on slope angle, aspect, altitude and curvature was obtained from a digital elevation model (DEM) in GIS (ESRI ArcMap 9.3). The DEM was derived from a 1:20,000 scale topographic map; equidistance: 10 m. Digitized data on lithological layers and dip were provided by Jarðfeingi. Land-use information was obtained from Thorsteinsson (2001, 2007), which contain information on different land-use areas and the spatial distribution of sheep grazing in the past 40–50 years. Since the spatial distribution of grazing sheep has proved reasonably unchanged through time, a sheep density index (SDI) was developed to signify the number of mother-sheep per km 2 of the study area.

5

4.3.3. Data pre-processing Data on all preparatory factors were stored in raster layers. Information on slope angle, aspect, altitude, lithology and land use was stored in 5 m × 5 m grid cells which thus became the slope unit in the statistical analysis. Slope curvature data were stored in 50 m × 50 m grid cells, for optimal capture of curvature elements in the landscape. Data from a total of 1314 (219 unstable and 1095 stable) grid cells were extracted for the DFA. Each of the 219 unstable grid cells represented the centroid of one of the debris-slides in the study area and was selected from centroid point coordinates of debris-slide scar polygons in GIS. Choosing only one grid cell instead of all in each debris-slide scar polygon was done to prevent spatial autocorrelation (Van Den Eeckhaut et al., 2006). Moreover, at each debris-slide scar polygon, 25 m buffer zones were established to ensure that stable grid cells were not selected too close to slope failure areas. The 1095 stable grid cells, which corresponded to five times the number of selected unstable cells, were randomly selected using the Create Random Points and Sample functions in ArcMap 9.3. The 1:5 relationship between unstable and stable grid cells was chosen to obtain a large representative dataset with a balanced set of stable/ unstable grid cells (King and Zeng, 2001; Chau and Chan, 2005; Van Den Eeckhaut et al., 2006). As stated by Quinn and Keough (2002) input variables in DFA must be continuous and normally distributed. However, Carrara et al. (2008) and Van Den Eeckhaut et al. (2009) successfully applied DFA in landslide research using binary data. In this study, seven preparatory factors were included in the DFA as eight continuous variables, while two could not be converted to continuous data and were included as binary variables. A description of the variables included in the DFA is seen in Table 1. Normality of continuous variables was tested by use of probability plots, and the variable ALTITUDE was subsequently square-root transformed to fit a normal distribution. Although the variables ASPECT EW, PLAN CURVE and PROF CURVE could not become perfectly normal distributed, their contribution in the DFA was still analyzed. This procedure has earlier been adopted by Baeza and Corominas (2001). 4.3.4. Modeling procedure Data from the 1314 grid cells were imported into the statistical program SYSTAT (www.systat.com). The DFA was run as a stepwise backward procedure. This means that initially all variables were included in the discriminant model, and at each step the variable contributing least to the prediction of group membership was removed. Consequently, only the variables contributing most to the discrimination was kept in the model. The probability of entering/removal of each variable, indicating its statistical significance in the discrimination, was set to 0.15. Model calibration was done from 65% of the grid cells, which were randomly selected in the program, while the remaining 35% of the grid cells were used for validation. The 65%/35% proportion was chosen as a compromise between having a large amount of training data and a sufficient dataset for validation. 5. Results and discussion 5.1. Basic inventory characteristics A total of 219 debris-slides were identified in the study area with SA varying from 5.6 to 2106.9 m 2, (Table 2). Magnitudes were remarkably small compared to results in Hungr et al. (2008), who found SA values from 100 m 2 to 22 000 m 2 in British Columbia, Canada. Most debris-slides occurred as new slope failures, while only few were retrogressive movements of existing failures. Of the 219 debris-slides, 84% developed into debris-avalanches, while 16% developed into debris-flows (Table 2). The quality of the inventory is considered high for several reasons. The low vegetation within the study area clearly demarcated debris-slide

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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Table 2 Basic debris-slide characteristics. Number of debris-slides (n) Magnitude of debris-slides (SA)

219 5.6–2106.9 m2

Characteristic Debris-slide was new slope failure Debris-slide was retrogressive movement of existing slope failure Debris-slide developed into debris-avalanche Debris-slide developed into debris-flow

Number 214 5

% of n 98% 2%

183 36

84% 16%

scars and diminished the bias from nonregistered events hidden under forest canopy, an issue addressed in other studies (Brardinoni et al., 2003; Brardinoni and Church, 2004; Miller and Burnett, 2007; Turner et al., 2010). The cool temperate climate slowed down the overgrowth of old debris-slide scars, which were thus clearly visible. Moreover, as pointed out by Galli et al. (2008) as quality improving elements when preparing landslide inventories, medium to large scale photographs were used for the API in combination with fieldwork and additional debris-slide information. 5.2. Magnitude frequency analysis A plot of the MCF relationship shows a decrease in debris-slide frequency with increasing magnitude (Fig. 4). The MCF curve shows three distinct characteristics, which resembles what is seen in other landslide studies, regardless of whether magnitude is measured as area or volume of landslide scar or of the entire landslide. Above a certain magnitude the MCF relationship can be described by a mathematical power–law. At lower magnitudes the power–law model is no longer valid, since the MCF curve flattens out. The point at which the MCF relationship flattens out is known as the roll-over (Fig. 4). In this study the roll-over occurs at 100 m 2 (Fig. 4), above which debris-slide frequency can be predicted by the power–law function Y ¼ 936:26X

−1:277

2

; r ¼ 0:98

ð6Þ

which includes app. 50% of the identified slope failures. There is a disagreement among researchers on what causes the roll-over at small landslide magnitudes. Brardinoni and Church (2004) exploring the magnitude–frequency relationship of shallow landslides in southwest British Columbia, Canada, argued that a roll-over of landslide volumes below 1600 m3 was due to undersampling in API. The same argument was used by Stark and Hovius (2001) who analyzed two landslide datasets from the Southern Alps, New Zealand. Roll-over

of landslide areas below 797 and 1781 m2 was due to resolutions of the aerial photographs employed. In contrast, Guthrie and Evans (2004), deriving an MCF curve for debris-slides and debris-avalanches on Vancouver Island, British Columbia, Canada, observed a roll-over at 10 000 m2 for landslide areas, well above the minimum resolvable size of their aerial photographs (500 m 2). Consequently, a physical explanation was favored for the roll-over. Similar conclusions were reached by Martin et al. (2002) and Guzzetti et al. (2002). In the latter study, Guzzetti et al. (2002) provided the explanation that small shallow landslides are prevented by cohesion in the soil, which provides strength sufficient to persist slope movement. With 1:15,000 as the minimum scale of analogue aerial photographs in this study, an SA of 100 m 2 corresponds to 44.4 mm2 and an SA of 10 m 2 corresponds to 4.4 mm2 when observed with the 10× magnifying glass used. Debris-slides of such magnitudes were clearly detectable on analogue as well as on digital aerial photographs, with the latter having pixel sizes from 0.4 to 0.5 m. Taken into consideration that slope failures related to coastal erosion and aeolian and wash transport processes were excluded in the analysis, a physical explanation is strongly favored for the roll-over in this study. Debris-slides at small magnitudes are believed to be less frequent, since small potential slope failures are held in place by the strength added by surrounding soil and roots. Thus, we support the physical explanation for the roll-over given by Guzzetti et al. (2002) above. With increasing magnitude of the potential debris-slide, the sliding movement is easier initiated, however depending on the specific rainfall/snowmelt event and local preparatory factors. As seen on the MCF curve, the largest debris-slides show a steepening trend, which is also observed in Martin et al. (2002) and Hungr et al. (2008). The steepening behavior is believed to show a limitation of the Faroese landscape to generate very large debris-slides. This argument is supported by comparing Fig. 4 to the largest debris-slide known in the Faroe Islands. The ~4000 m2 slope failure which is by far the largest registered event and thus a very rare phenomenon would still appear below the power–law function in Fig. 4. Further research is however needed to clarify if the limitation in magnitude is caused by the dimensions of the landscape, distance between rocky outcrops or subsurface geological breaks in slope, or perhaps hydrological factors. As described in Section 3, debris-slides which develop into debris-avalanches generally maintain their initial volumes, while debris-slides which transform into debris-flows can increase in volume by erosion of bed material along their runout path. With most debris-slides from the inventory developing into debris-avalanches (Table 2), the MCF relationship gives a good indication of how often debris-avalanches of certain magnitudes occur within the study area. For obtaining equivalent results for debris-flows additional work is required to (1) identify other phenomena generating debris-flows, such as rockfall, as described in Hungr et al. (2008) or (re)mobilization of deposited material in drainage lines (Dahl, Unpublished results), and (2) quantify the increase in volume from erosion of bed material. 5.3. Discriminant function analysis The DFA was able to correctly classify 69% of the calibration grid cells and 70% of the validation grid cells into their pre-determined groups (Table 3). The classification rate for the calibration data is stable at 69%, while the rate for validation data varies from 69% to 73%. The discriminant function with the constant A, the contributing variables kept in the model through the stepwise backward procedure and the unstandardized discriminant function coefficients for each variable can be written as

Fig. 4. MCF relationship of the 219 debris-slides.

DS ¼ −3:066 þ 0:04 SLOPE þ 0:015 ASPECT NS þ 0:526 PLAN CURVE þ 0:034 SDI−0:042 Sqr ALTITUDE ð7Þ

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

M.-P.J. Dahl et al. / Geomorphology xxx (2012) xxx–xxx Table 3 Confusion matrix indicating model performance of the DFA. Actual group membership Predicted group membership Stable grid cells Unstable grid cells Calibration data Stable grid cells Unstable grid cells Overall grid cells correctly Validation data Stable grid cells Unstable grid cells Overall grid cells correctly

69% 31% classified: 69% 69% 27% classified: 70%

31% 69% 31% 73%

As seen in Eq. (7) and from the SDFC values in Table 4, the most important preparatory factors for determining spatial debris-slide distribution in the study area are aspect in the north-south direction, slope angle, sheep density, plan curvature and altitude. Conversely the influence of aspect in the east-west direction, lithology, dip, profile curvature and differences in infield/outfield areas is insignificant, since these variables have been removed during the stepwise backward selection procedure. Debris-slide occurrence is highest on southern facing slopes with increasing slope angle, sheep density and slope divergence and most infrequent in high-altitude areas of the landscape. Increase of debris-slides with slope angle is in good correspondence with other observations in the Faroe Islands (Dahl, 2007; Dahl et al., 2010) and is seen in countless studies on shallow landslides (e.g. Baeza and Corominas, 2001; Dai and Lee, 2002; Zêzere et al., 2004) as the result of increasing driving forces at the potential slip surface. Frequent debris-slide occurrence on southern slopes which are highly exposed to sunlight is consistent with results from Dai and Lee (2002), who mapped 2135 translational landslides on Lantau Island, Hong Kong. However, other studies have reported that landslides are most abundant on shaded slopes. Gao (1993) argued that high landslide occurrence on shaded slopes could be due to elevated soil moisture contents caused by local precipitation patterns and less solar radiation. Elevated soil moisture contents on shaded slopes was supported as an explanation for high landslide occurrence by Lan et al. (2004) and Sidle and Ochiai (2006). One explanation for the high debris-slide occurrence on sunny slopes could be that soil cracks during drought periods are more abundant here than on shaded slopes. Consequently, during rainfall water can more easily infiltrate the soil, reduce apparent cohesion or build up positive pore water pressures at potential slip surfaces. However, further analysis is needed to better understand these processes. Future studies could also focus on investigating if aspect in the north-south direction reflects dominant precipitation directions, which could explain the frequent debris-slide occurrence on southern slopes. In contrast to aspect in the north-south direction, aspect in the east-west direction has been rejected from the discriminant function.

Table 4 Result of the DFA. Preparatory factor

Variable in DFA

Slope angle Aspect

SLOPE ASPECT NS ASPECT EW Sqr ALTITUDE LITHOLOGY LITHO DIP PLAN CURVE PROF CURVE SDI LAND FIELD

Altitude Lithology Dip Plan curvature Profile curvature Sheep density Infield/outfield Constant A

Wilks-λ: 0.901, app. F: 18.641, df: 5,853, p b 0.0001.

SDFC 0.559 0.646 −0.242

0.311 0.465 −3.066

7

There are two possible explanations for this. One is that aspect in the east-west direction is simply not important for determining the spatial distribution of debris-slides, since it is not a significant proxy variable for insolation, soil moisture content or dominant precipitation direction. The second is that the model does not capture the significance of the variable, since it is not perfectly normal distributed, cf. Sections 4.3.3, but exhibits an inverse bell distribution. If the latter explanation is correct, it underlines the importance of using only normal distributed data in DFA. Assuming that sheep grazing is directly correlated with sheep density, the result shows debris-slide occurrence to increase with grazing intensity. The result supports the argument in Nordic Council of Ministers (2007) that grazing from domestic animals is believed to increase soil erosion in the Nordic Countries. Most studies investigating the correlation between grazing and landslide occurrence work with the conversion from forest to grassland. Consequently, papers dealing with consequences of different grazing intensities solely on grasslands are very few. Meusburger and Alewell (2008) showed that increasing shallow landslide occurrence in the Swiss Alps through a 40 year study period could be related to increased grazing from sheep and cattle. Conversely, Tasser et al. (2003), also working in alpine environments, observed a lower landslide occurrence in grazed areas compared to non-grazed abandoned areas. The result was explained by differences in plant communities as well as shorter root lengths and lower root densities in abandoned areas. Fosaa and Olsen (2007) showed that height and ground cover of vegetation in the Faroe Islands was reduced from sheep grazing. Consequently, the observed increase in debris-slide occurrence with grazing intensity could result from lower below ground biomass and thus lower slope stability. However, further research is needed to understand the relationship between grazing and vegetational response. Increasing debris-slide occurrence with slope divergence contradicts results from Gao (1993) who found a high susceptibility of translational landslides on convergent slopes compared to other slope types. Also, Sidle and Ochiai (2006) argued that since subsurface water is more easily concentrated on convergent hillslopes, these are more susceptible to landslides as compared to divergent and planar slopes. One explanation for the result could be that divergent slopes are exposed to aeolian processes which thus remove vegetation. The lack of vegetation may decrease root strength in the soil and increase debris-slide frequency. However, further research is needed to understand these processes in the Faroese landscape. In spite of results from Aune and Førland (1986) which indicate that precipitation in the Faroe Islands may increase by 34% per 100 m above sea level, debris-slide occurrence in this study decrease with altitude. The smaller number of debris-slides in high-altitude areas of the landscape is consistent with results from Lan et al. (2004), who mapped 574 rainfall-induced landslides in Yunnan area, China. Although precipitation may be increasing with altitude, there are several possible explanations for the low debris-slide occurrence in high altitudes of the study area. First, with increasing altitude, rocky outcrops become more dominant in the landscape, lowering the availability of landslide material. Secondly, during the API procedure, small debris-slide-like features occurring in non-vegetated high-altitude areas were interpreted as being more related to aeolian and wash transport processes than to landslide activity. The DFA model performance of app. 70% is only moderate compared to Baeza and Corominas (2001), Carrara et al. (2008), Van Den Eeckhaut et al. (2009) and suggests two important characteristics of debris-slide activity in the Faroese landscape. Either it is difficult to correctly identify stable slopes since debris-slide activity is widespread throughout the Faroese landscape, additional preparatory factors have to be included in the DFA to improve its performance or a different type of slope unit, other than grid cells, has to be used for the analysis. The former is strongly supported by field observations and API in this paper; besides from debris-slides included in the present inventory, older

Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015

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M.-P.J. Dahl et al. / Geomorphology xxx (2012) xxx–xxx

Fig. 5. (A) Aerial photograph of the study area from 1958. (B) Aerial photograph of the study area from 2002. All debris-slides seen in (B) (except one, marked with a circle) occurred prior to 1958 and are widespread throughout the landscape.

slope failures prior to 1958 are widely seen throughout the landscape, as exemplified in Fig. 5. In an attempt to improve model performance, preparatory factors such as distance to upslope rocky outcrops and soil depth could be considered. Glade (2005) and Tarolli et al. (2008) described how upslope rocky outcrops can lead water through small steep drainage lines into slopes below, thereby triggering shallow landslides. Since rocky outcrops are dominant features within the Faroese landscape (Fig. 5) their role in facilitating debris-slide initiation could be considered. There are different indications in the literature on how soil depth affects spatial landslide occurrence. Santacana et al. (2003) showed through DFA that increasing soil depth was the second most important preparatory factor for explaining shallow landslide distribution. High landslide occurrence with increasing soil depth was also observed by Tasser et al. (2003) and Zêzere et al. (2004). On the other hand, Fuchu et al. (1999) argued that more rainfall is required to saturate soils with increasing depths regardless of the initial degree of saturation. Soil depth is very challenging to map and is therefore often ignored as a preparatory factor in regional landslide studies. As seen in Dahl (2007) soil depth in the Faroe Islands varies a great deal, even at the micro scale. Future investigation of soil depth as a potential preparatory factor for debris-slide activity in the Faroe Islands therefore depends on the ability to accurately map this parameter. In general, more research is needed in the Faroe Islands before the hazard from debris-avalanches and debris-flows can be quantified. Model performance of the DFA needs to be improved by either testing more preparatory factors or by using slope units other than grid cells. By for example delineating slope unit polygons by use of drainage lines and divides in the landscape, geomorphological and hydrological characteristics could be captured for whole slopes instead of only for individual grid cells, Guzzetti et al. (2006), Carrara et al. (2008), Van Den Eeckhaut et al. (2009). Since the derived MCF relationship primarily is valid for debrisavalanches, other phenomena generating debris-flows (e.g. rockfall or mobilization of deposited material in drainage lines) must be identified as well as the increase in volume during debris-flow runout. Subsequently, runout zones for both debris-avalanches and debris-flows must be outlined for example by applying the modified angle of reach method presented in Dahl et al. (2010) supported by numerical runout analysis. However, by quantifying magnitude, frequency and important preparatory factors for debris-slides in a limited study area, this study has provided essential information to the ongoing landslide risk-assessment project in the Faroe Islands.

6. Concluding remarks To provide data for hazard and risk assessment of debris-avalanches and debris-flows in the Faroe Islands, this study has aimed at quantifying the magnitude and frequency of debris-slide origins as well as identifying which preparatory factors are responsible for spatial debris-slide distribution in the landscape. For that purpose a debris-slide inventory has been generated, covering a 159 km2 study area over a 51 year period in the northern Faroe Islands. Results from a magnitude–frequency analysis show that debris-slides larger than 100 m2 can be predicted from the power–law function: Y=936.26X−1.277, r2 =0.98. A physical explanation is preferred for the roll-over pattern of smaller slope failures. Discriminant function analysis shows that preparatory factors responsible for spatial debris-slide distribution are aspect, slope angle, sheep density, plan curvature and altitude, while influence of lithology, dip, profile curvature and differences in infield/outfield areas are negligible. 7. Acknowledgements This study has been carried out in cooperation between Department of Environmental, Social and Spatial Change, Roskilde University, Denmark and Jarðfeingi (Faroese Earth and Energy Directorate), the Faroe Islands. Moreover, funding was provided by the Danish Agency for Science Technology and Innovation, Case no. 09-063155. Aerial photographs were provided by the Danish National Survey and Cadastre and the Faroese Environment Agency. Furthermore, the authors wish to thank Dr. Esbern Holmes for technical GIS assistance, Dr. Gary Banta for statistical assistance and Ritta Bitsch for graphical preparations. References Aune, B., Førland, E.J., 1986. Nedbør på Færøyene – vurderinger i forbindelse med vannkraftutbygning på Eysturoy. Technical Report. Norwegian Meteorological Institute, Oslo, pp. 27–86 (in Norwegian). Avanzi, G.D., Giannecchini, R., Puccinelli, A., 2004. The influence of the geological and geomorphological settings on shallow landslides. An example in a temperate climate environment: the June 19, 1996 event in northwestern Tuscany (Italy). Engineering Geology 73, 215–228. 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, 15–31. Baeza, C., Corominas, J., 2001. Assessment of shallow landslide susceptibility by means of multivariate statistical techniques. Earth Surface Processes and Landforms 26, 1251–1263. Brardinoni, F., Church, M., 2004. Representing the landslide magnitude–frequency relation: Capilano river basin, British Columbia. Earth Surface Processes and Landforms 29, 115–124.

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Please cite this article as: Dahl, M.-P.J., et al., Magnitude–frequency characteristics and preparatory factors for spatial debris-slide distribution in the northern Faroe Islands, Geomorphology (2012), http://dx.doi.org/10.1016/j.geomorph.2012.09.015