Precipitation as a Driving Factor for Snow Avalanches: A 46-year Case Investigation of Extreme Events in the French Alps

University of Amsterdam June 2018 Bachelor Thesis – Final Paper

Precipitation as a Driving Factor for Snow Avalanches:

A 46-year Case Investigation of Extreme Events in the French Alps

Skieur.com

Supervisor: Dr. Ir. J.H van Boxel Yoram Terleth

Abstract

The French Alps are undergoing a trend towards more frequent and more intense precipitation events. One of the consequences of this trend might be increased snow avalanche activity during the wintertime, increasing hazard for local populations and infrastructure. The aim of this study is to establish the effects of changing precipitation patterns on snow avalanche occurrence in the French Alps over the last 50 years. To achieve this aim, the study analyses and compares a 47-year climate record from the Embrun weather station with an adaptation of the EPA avalanche database on the local scale, investigating the links between heavy snowfall and avalanche cycle occurrence. It finds precipitation to be the main driver of avalanche occurrence, with snowfall maxima preceding avalanche cycles by an average of two days. Other factors such as temperature and snowpack structural weakness are found to have a non-negligible influence, but to a much lesser extent. An analysis over time shows a strong bias in the used avalanche database, which is thought to reduce correspondence between avalanches and precipitation. No increase in extreme precipitation event frequency or intensity is witnessed. A comparison of precipitation in Embrun and spatial averages over the French Alps shows severe discordance, implying Embrun might be subject to a different precipitation and thus avalanching regime than other regions in the French Alps. The observed link between precipitation and avalanches suggests that more research regarding local change in extreme precipitation occurrence under climate change and their effect on avalanche behavior would be highly relevant in both climate research as well as hazard assessment and forecasting.

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1. Introduction

Changes in earth’s climate are anything but uniform: although a warming trend has been witnessed during the last century, local effects of a changing climate are diverse and usually much more complex than simple warming (Houghton, 2015). According to the IPPC’s fifth assessment report (IPCC, 2014 - p.41), Western Europe is undergoing an increase in precipitation, with a trend towards more intense rainfall events (IPCC, 2014 - p.58). A similar trend was noted in central Europe (Alewijnse, 2004) as well as in the European Alps and more specifically the French Alps (Nuissier et al, 2011; Gaume et al., 2013).

Snow avalanches occur frequently in the French Alps and are subject to intense monitoring and mitigation programs. Barriers aimed at protecting infrastructure are common in inhabited alpine landscapes, and both private industries such as ski resorts and local governments finance extensive mitigation programs aiming at preventing accidents by triggering avalanches intentionally. Despite this attention, several accidents occur every year ranging from isolated incidents involving winter recreationalists to large scale natural disasters (ANENA, 2018). Although the processes involved in avalanche dynamics are reasonably well understood, their modelling remains a challenge, and forecasting their occurrence consists of “educated guesswork” (Jamieson et al., 2008). Several studies have shown that rising temperatures could lead to increased avalanching (Naaim et al., 2013; Ballesteros-Canovas et al., 2018), but little research has been conducted towards influence of climate change on avalanches through changing precipitation regimes. Among factors driving avalanche occurrence however, precipitation is perhaps the most important, especially when considering large scale avalanches (Eckert et al., 2010).

As such, it seems interesting to consider whether changes in precipitation patterns during winter in the French Alps translate to changes in avalanche activity. Naturally triggered large scale avalanche cycles have been shown to be strongly linked to precipitation under certain conditions, classifying as direct-action avalanches (Hendrikx et al., 2005). The aim of this study is to establish the effects of changing precipitation patterns on snow avalanche occurrence in the French Alps over the last 46 years. The study would achieve this aim through firstly establishing a relation between precipitation and avalanche events, by investigating the relation between three known avalanche drivers and avalanche cycle intensity. Secondly the study assesses changes in, and possible links between, the occurrence frequency of extreme precipitation events and avalanche events over the last 50 years.

2. Theoretical Setting 2.1 Precipitation

The French Alps are the south western section of the European Alpine chain; they reach from the Chablais Massif at the border between France and Switzerland along the Italian border to the Mercantour Massif, almost touching the Mediterranean Sea. The westernmost front ranges have generally lower elevations, and the highest massifs are located further east, close to the Italian border (Durand et al., 2009). The high latitudinal range of the chain causes large differences in summer climate due to the influence of the Mediterranean in the southern regions; this difference is less pronounced in winter, but still results in higher freezing levels in most southern areas (Ancey, 1998). Two typical meteorological situations (circulation types) tend to bring precipitation to the area in wintertime. Northwesterly winds bring moisture from the Atlantic in the form of frontal perturbations, which tend to affect most of the French massifs but with a more intense effect on the westernmost ranges (Ancey, 1998). This results in these ranges receiving the highest amount of winter (Nov. – Apr.) precipitation at 1800 m a.s.l. (Durand et al., 2009). Despite the dominance of northwesterly flows, a second circulation type needs to be considered: south easterly flows can occur occasionally in the southern parts of the French and Italian Alps, supplying large amounts of moisture from the Mediterranean and Po plain (Nuissier et al, 2011). In winter this can lead to very intense precipitation episodes, resulting in high quantities of snow accumulation over short periods of time (Gaume et al., 2013; Eckert et al., 2010). The effect of these “grosswetterlagen” on snowfall in the French Alps is reflected by Gaume et al. (2013): although fixed altitude precipitation totals are generally higher in the northwestern massifs, the southeastern massifs such as the Mercantour, Queyras and Ecrins tend to have higher snowfall extremes. Despite the general trends outlined above, it is important to note that mountainous regions are characterised by large spatial variations in precipitation (Phillips et al. 1992). Orographic effects are strong and can cause steep gradients over short distances, effects of altitude on temperature and precipitation can differ per location, and many micro-climates have been observed (Ancey, 1998).

According to the IPCC’s fifth assessment report (IPCC, 2014. p.58), increases in overall precipitation as well as increased temporal clustering of precipitation are expected over western Europe. Extreme events, such as high intensity precipitation, are likely to become more intense and occur more frequently in the French Alps (Castebrunet et al., 2012), with winter storms from the west gaining intensity and the easterly winds gaining more moisture over a warmer Po plain and Mediterranean. Although these trends are subject to much research in their effects on Western Europe, fewer studies investigate their occurrence specifically in the Alps (Castebrunet et al., 2012; Isotta et al., 2013) This is likely to be caused by the difficulty of assessing representative trends in such heterogeneous terrain as the French Alps.

2.2 Avalanche Activity

Just like small scale spatial variation in precipitation, snow avalanches are a very complex natural phenomenon. Although the processes creating avalanche prone conditions are relatively well known and extensively studied, it is impossible to predict avalanche occurrence with certainty as the precise dynamics are unique to each event (McClung & Schaerer, 2006). Dynamic models based on Voellmy-fluid behavior have been in existence since the 1950’s, but little progress seems to have been made since then and they are still generally considered as insufficient (Jamieson et al., 2008). Statistical models have been widely used to establish local hazard maps (Jones & Jamieson, 2004) as well as studies monitoring region wide avalanche activity over time (Eckert et al., 2013; Castebrunet et al., 2012). In general terms, avalanche occurrence is driven by instability resulting from a combination of

meteorological factors and terrain features (McClung & Schaerer, 2006). An overview of these factors is given in table 1. The contribution of each effect to the overall degree of instability of the snowpack and ultimately the release of a snow avalanche depends on conditions and is unique to each case. However, several types of avalanches are discernable, and each type tends to have an associated main driver (McClung & Schaerer, 2006). Direct action dry snow avalanches (table 1) are perhaps the most strongly linked to precipitation, as they are a form of slab avalanche (table 1) where the avalanching layer consists entirely of freshly fallen snow and avalanches because of the loading on a weak layer lying at the upper surface of old snow (the top of the snowpack directly before the start of the precipitation episode) (Schweizer, 1999; Hendrikx et al., 2005). Avalanches of this type usually occur in cycles during or within a few days after a heavy snowfall (Eckert et al., 2010; Hendrikx et al., 2005) and trigger naturally under the loading of the added snow as it settles. Because of this strong link to snowfall, trends in precipitation events are likely to be reflected by trends in occurrence of direct action avalanches. If direct action avalanches are the dominant form of avalanching in the area, it is likely that these trends also extend to general avalanche cycle occurrence and intensity in the French Alps.

Avalanche Type Primary driver of

Instability Secondary Driver of Instability Further Drivers Dry slab direct action Fresh storm snow

loading Wind loading Snowpack weaknesses, temperature, snow coherence and moisture content, unnatural loading etc.

Dry slab cumulative Snowpack weaknesses Supplementary

loading Wind, temperature, snow moisture content, storm snow loading, unnatural loading, etc.

Wet loose Temperature Snow moisture

content Ground surface, snowpack structure, unnatural loading Wind slab Wind loading Storm snow loading Snowpack structural

weaknesses, temperature, unnatural loading, snow moisture content

Table 1: (Based on text McClung & Schaerer, 2006; assembled for this study) Examples of avalanche types and a non-exhaustive ranking of their possible main, secondary and further drivers. These are examples and, as each avalanche prone instability situation is unique, do not represent a generality. Their intent in this study is to provide some oversight towards avalanche types and the possible circumstance leading to their type of instability. Slope angle is the essential driver of each type of avalanche, but it is not included in this table as it does not change in one track on the studied time scale.

3. Methods 3.1 Datasets

Studies investigating the relations between avalanche occurrences and climatic change on larger scales generally choose to use dynamic model outputs (Durand et al., 1999) for snow and weather data (Castebrunet et al., 2012; Jomelli et al., 2007). Meanwhile, studies focussing on regional scales usually prefer data from the instrumental record (Hendrikx et al., 2005) or a combination of measured and modelled data (Eckert et al., 2010). This type of data is favored in these cases because the absence of interpolation allows for higher accuracy (Jomelli et al., 2007), which is necessary due to the strong spatial variability of precipitation in the Alps (Durand et al., 2009). This study focusses on a local scale, so it uses precipitation and temperature data from the Embrun weather station, located in the Hautes Alpes, France (Table 2). The Embrun instrument record provides daily values since 1870, with virtually no missing values since 1950, which makes it very suitable for the objectives of this study.

STAID SOUID SOUNAME CN LAT LON ELEV. ELEI BEGIN END PARID PARNAME

755 104112 EMBRUN FR 44:33:56 006:30:08 871 RR9 18770101 20171231 10 Jean-Michel Soubeyroux Table 2: Metadata provided for Embrun weather station instrument record (Klein Tank et al, 2002).

Due to the inherent dangers of winter travel in mountainous terrain (McClung & Schaerer, 2006) relatively few time-series data on the occurrence of avalanches exist in general (Ballesteros-Canovas, 2018; Castebrunet et al., 2012). Most avalanche databases are very recent, and often incomplete. For this reason, past studies have relied on proxy data methods such as dendrochronology to construct a record of past avalanche activity (Ballesteros-Canovas, 2018; Christophe, 2010). However, such methods have significant drawbacks: dendrochronological resolutions never achieve higher than one year, and geomorphological evidence also often lacks accuracy (Decaulne & Sæmundsson, 2008). Perhaps the best available database of direct observations is the “Enquête Permanente sur les Avalanches” (EPA, 2018). This database assembles observations occasionally dating back to the early 1900’s covering approximately 5700 avalanche paths throughout the French Alps and Pyrenees, and over 75000 events as of 2002 (Garcia & Bélanger, 2002). As this study considers avalanche behavior over time in a relatively small area, the EPA is quite well suited for its purposes (Castebrunet et al., 2012): the database is utilised on a small scale, considering 25 avalanche paths in proximity to Embrun. It considers these tracks over a timespan of 46 winter seasons, from December 1971 to April 2017.

3.2 Track Selection and Location

The selection of avalanche paths to consider was based on the following criteria: a relative proximity to the Embrun weather station to ensure its data is representative, an average starting zone altitude ranging between 2000 and 2700 m a.s.l. to allow for universal temperature correction, and an attempt has been made to select a range of paths facing all aspects to eliminate possible biases. Paths with lacking data, or unprecise date of avalanche occurrence recordings were obviously excluded. This selection is based on annotations and metadata provided with the EPA database, as well as the locational maps (figure 1): paths in proximity to infrastructure such as roads or buildings are most likely to comprise an accurate record of avalanche events (Ancey, 1998). Avalanche paths visible from recreational trails might have biased records as human frequentation of these areas increased significantly in recent years (Ancey, 1998). An overview of selected tracks and their main characteristics is given in Appendix 1.

Figure 1: Example Location map showing the village of Embrun and close by monitored avalanche tracks. The geographic closeness allows for comparison between precipitation and avalanche data and the diversity of aspects cancels the influence of wind transport. Visibility from infrastructure allows for a more accurate record, and distribution over aspects lowers bias resulting from wind loading and ensuing avalanching. Approximate location of Embrun weather station shown with red X at bottom right of image. (EPA, 2018).

3.3 Avalanche Selection, Data Format Conversion

A challenge of using the EPA is the format available online: the avalanches are recorded by hand on field notebooks and typed in on the computer to be converted to PDF files, which are uploaded to the database (Garcia & Bélanger, 2002). This format has obvious limitations for analysis and the recorded event were transferred by hand towards Microsoft excel. Tracks were represented by columns while all dates (each day from December 1st _{to April 30}th _{the next year) were represented through rows,}

with ten rows left blank in between seasons to prevent inter seasonal interference during subsequent analysis. As outlined in table 1, wet snow avalanches undergo very little influence from snowfall (Naaim et al., 2016): the choice was made to differentiate this type of avalanches and a supplementary table was made to allow for a possible distinct analysis. Indexing methods on this table remained the same.

Avalanche events described in the EPA were reported by inscribing a “1” on the corresponding (date, path code) coordinates in the excel sheet. Events were inscribed in the dry snow avalanche side unless specifications given in the EPA indicated their cause of triggering to be clearly linked to warming or meltwater, in which case the event was inscribed in the table for wet snow avalanches. As the categories are mutually exclusive (Hendrikx et al., 2005; Naaim et al., 2016), each event could only be inscribed once. Events caused by anthropogenic intentional or unintentional triggering were excluded. The converted dataset and its metadata as well as workings and outputs are available in Appendix 2.

3.4. Index Calculations

The conversion from a matrix of logical elements specifying avalanche events to a measure of avalanche cycle intensity over the area is attained through the calculation of an index as given by Eckert et al., 2010:

𝑓 =𝑛𝑖 𝑐

With fi the average number of avalanches per path and per day over a 3-day period, from the day prior

to the day after. Ni the total amount of avalanches during the 3-day period and Ci the total amount of

tracks (multiplied by the 3-day period in this case). Values will range between 0 and 1, resulting in a time-series of daily percentages describing 3-day cycle intensity. The index is calculated for all events (wet snow and dry snow) as well as for both types separately.

3.5. Drivers

Three of the main drivers towards avalanche activity are investigated: precipitation, temperature and upper snowpack structural weakness. Precipitation is the focus of the research and is the first investigated driver. The data from the Embrun weather station is used directly: no adjustment for altitude needs to be made because only relative precipitation intensity is required for the analysis techniques used in this study.

Temperature, the second driver, is monitored with data from the Embrun station, adjusted along a 0.6˚C decrease per 100 m altitude gain (Christopherson & Birkeland, 2016: p.153) to the average start zone altitude of 2500 m a.s.l.

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑇𝑒𝑚𝑝(𝑖) = 𝑇𝑒𝑚𝑝(𝑖) + [0.006 × (2500 − 871)]

A third predictor used in this study attempts to account for weather dependent snowpack stability and is monitored through combining both meteorological datasets. The presence of faceted snow on top of the snowpack is a source of instability and can be a cause for the avalanching of subsequent fresh snow (figure 2): such layers are classified as persistent weak layer forms (McClung & Schaerer, 2006: p.67). The instability of such weak layers originates in the low inherent cohesion of these persistent forms (facets and surface hoar; figure 3), which is caused by growth of the crystals towards their edges, in turn induced by a strong thermal gradient in the snowpack (McClung & Schaerer, 2006: p.p. 55-60).

As temperatures in the lower half of an alpine seasonal snowpack remain constant and close to 0˚C, strong gradients generally occur close to the snow surface and intensify with cold surface temperatures, while gradients are reduced by the deposition of fresh snow (McClung & Schaerer, 2006: p. 53). This study proposes an index factoring temperatures and precipitation over a ten-day period preceding any day in the time-series:

𝑊𝑒𝑎𝑘 𝑙𝑎𝑦𝑒𝑟 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒 𝐼𝑛𝑑𝑒𝑥 (𝑖) = 1 − [∑ 𝑝𝑟𝑒𝑐𝑖𝑝 max 𝑝𝑟𝑒𝑐𝑖𝑝 +

𝑚𝑒𝑎𝑛 𝑡𝑒𝑚𝑝(𝑖 − 10: 𝑖)

max 𝑡𝑒𝑚𝑝 ]

The higher the resulting index on any given day, the more potential there is for a weak layer being present at the upper section of the snowpack on that day, and the higher ensuing instability during and after the next snowfall.

3.6. Linking Avalanche Cycles and Possible Drivers: Cross Correlation

Cross correlation tables are constructed using Microsoft excel to calculate both the correlations of both direct-action avalanche cycle and total avalanche cycle over time lags ranging from -10 to +10 days. Correlation is calculated with the three previously explained types of predictors. Supplementary cross correlations will also be conducted for the first and second halves of the studied time period to verify possible changes in relations between driving factors.

Figure 2: Cross section of upper snowpack showing facets and surface hoar, two unstable persistent forms being covered by fresh snow. The weak layers are very likely to have formed during a cold dry period. (Gallatin National Forest Avalanche Center, 2018)

Figure 3: Faceted snow crystal. Growth after deposition occurred along edges due to strong thermal gradient in snowpack resulting in low cohesion shape. Original snowflake shape still visible. (Caltech.edu, 2018)

3.7. Precipitation and Avalanche Activity: Trend Analysis

A short MATLAB script is written to count and give a graphic representation of the occurrence of heavy snowfall events per season (Appendix 4). A study by Jomelli et al. (2007) considering avalanches in the Valloire valley finds a strong increase in avalanche triggering probability related to prior precipitation increasing in a range from 30 mm to 60 mm at the Valloire weather station (1470 m a.s.l.). These results incite the current study to investigate the occurrence of 30 mm, 40 mm and 60 mm 3-day cumulative precipitation. The moving 3-day value is used to ensure inclusion along date changes while retaining a one avalanche cycle timescale (Eckert et al., 2010). The number of avalanches (sum of total cycle intensity) occurring over the entire study area per season is also plotted to allow for a visual comparison with the number of intense precipitation events. A series of correlation coefficients is calculated with MATLAB for comparison of the two time-series. The usage of cumulative avalanche cycle index has the advantage of providing a straightforward value for total seasonal avalanche activity. However, it presents a slight risk of including cumulative avalanching and creating a disconnect between compared values when plotted next to seasonal extreme event frequency. A graphic comparison between seasonal occurrence frequency of days exceeding certain avalanche indices and of 3-precipitation exceeding thresholds values will be given in Appendix 6(b).

3.8. Precipitation Return Periods

Return periods are a statistical tool for assessing the occurrence frequency of events at certain thresholds of severity or intensity (Burt et al., 2009). Calculating the return periods of precipitation and their change over time will enhance the understanding of the Embrun precipitation regime. A short MATLAB script (Appendix 8(a)) was constructed to calculate monthly precipitation sums and to count days included in 3-day episodes exceeding various thresholds. Data from the Embrun weather station was used over a period from 1972 to 2011, the years 2012 to 2016 were left out of consideration in the MATLAB script as they included several NaN values. Year-round data instead of seasonal data was considered out of practical reasons also. This should be kept in mind but still allows for relevant conclusions regarding precipitation regimes to be drawn. Further calculations and construction of graphs were conducted in Excel (Appendix 2) along statistical guidelines by Burt et al. (2009).

3.9. Embrun Precipitation in Relation to Surrounding Area

A supplementary dataset of interpolated rain gauge point measurements towards a 5 km grid and at uniform altitude, compiled by Isotta et al. (2013), was shared by the Swiss federal office of Meteorology and Climatology (MeteoSwiss). This dataset is used to discuss the degree to which Embrun is a representative record for its indirect surroundings. For the purposes of the discussion, the daily values for the Embrun grid cell are compared with average values over an area delimited by the 46th _{parallel in the North and 44}th _{parallel in the South as well as and the 6}th _{and 7}th _{meridians (framing}

an area approximately covering the French Alps). All data used is obtained from the gridded dataset to ensure altitudinal consistency (Isotta et al., 2013). The nature of the dataset does not allow for straightforward data usage over long time periods, so this study settles for a comparison over the years 2001 to 2008. Year round rather than seasonal precipitation is analysed, as the goal of this short analysis is simply to place the Embrun precipitation regime in its broader context. The script for analysis can be found in appendix 7 (a).

4. Results

The objective of this study is twofold: determining whether precipitation can be considered a determining factor in the occurrence of avalanche cycles in the Embrun valley, and whether changing precipitation might result - or is resulting in increased avalanche activity around Embrun. The first paragraphs of this section will outline the outcome of the cross correlations used to determine relation between avalanches cycles and their driving factors. The second will investigate changes over time in both cycles and predictors. This section provides an overview of the outcomes: more detailed diagrams as well as data and cross correlation tables are available in Appendix 2.

4.1 Cross Correlation

Figure 4 shows a cross correlation diagram including correlations between all three predictors and the avalanche cycle variable considering all events, which also includes the significance envelope.

Figure 4: Output of cross correlation between avalanche cycle occurrence and possible driving factors. Correlation coefficient (R) plotted over time lag (days): positive lags represent avalanches occurring after the plotted factor while negative lags mean avalanches preceding the driving factor. A period of -10 to +10-day lag is shown. Values outside of the significance envelope (plotted in yellow) are significant.

When considering figure 4, all found correlations seem quite low, never reaching 0.2. However, significance is still achieved for all drivers during certain time lag intervals due to the high number of investigated values (sample size n= 7389 - Appendix 2).

Precipitation shows the highest correlation of all predictors, reaching its maximum at a time lag of +2 days. The curve drops quickly with lags tending towards zero, with correlation descending under the significance level at lag = -1 day and remaining insignificant as the lag decreases further. As time lag increases from +2, correlation also decreases strongly but shows a certain right skewness, descending under the significance level only at lag = 8 days. When translated to events recorded in the dataset, it

seems precipitation usually precedes avalanche cycles, which occur with the highest frequency two days after the most intense precipitation.

Temperature shows a negative correlation with avalanche cycle intensity throughout the studied lags, meaning low temperatures seem to occur most often along with avalanche cycles. The strongest correlation seems to occur at a lag of +4 days, and the lowest correlation occurs at lag = -1 day. This does seem to show a shift in temperature often occurring in the days preceding avalanche cycles. Correlation between the weak layer index and avalanche cycles is quite low throughout the studied lag period. The only significant correlation is negative, reaching its lowest value of -0.057 at lags between -1 and -2 days. This indicates a lower weak layer presence, or more upper snowpack stability, during the days following avalanche cycles.

Only minor deviations from the previously described observations are noted when conducting cross correlations for the first and second half of the period separately. These graphs are available in Appendix 3 for reference.

As described in section 3.3 of the methods, the transcription of avalanches from the EPA database to an excel format recorded avalanches in a separate category when characterised as wet slides. As the driving influence of precipitation on avalanche activity is the main focus of this study and precipitation is showing the highest correlation values in figure 4, the output of the cross correlation between precipitation and the two differentiated types of avalanche cycles (dry snow avalanches and wet snow avalanches) is presented in figure 5.

Figure 5: Cross correlation diagram showing correlation coefficients (R) between precipitation and dry snow avalanche cycle index over time in blue. Correlation coefficients between precipitation and wet snow avalanche cycle index is shown in orange and correlation between precipitation and total cycle index (including all events) is shown in grey. The curves show correlation over time lag: negative lags represent precipitation occurring before the plotted index while positive lags mean avalanches cycles preceding precipitation. A period of -5 to +5-day lag is shown.

The direct-action avalanche cycle index shows a correlation spectrum very close to the previously described total cycle index (shown in gray in figure 5): correlations are slightly higher at a lag of -2 days, reaching 0.205. In figure 4 negative lags signify precipitation preceding avalanching, as the avalanche cycle lags are constructed in reference to precipitation. Wet snow avalanche cycles show no significant correlation with precipitation.

4.2. Time-series Analysis

A series of detailed bar graphs showing the seasonal occurrence of various thresholds of extreme precipitation were produced as the output of the MATLAB script presented in Appendix 3.1. These graphs are shown in Appendix 5. Most relevant to this study is a comparison of these extreme precipitation occurrences and the seasonal sum of avalanche activity, as shown in figure 6.

Figure 6: (a) Seasonal count of days included in a 3-day precipitation event exceeding thresholds as given in figure legend. (b) Seasonal sum of 3-day avalanche cycle activity index. Seasons are shown on x axis depending on first studied season (dec.1971 - april 1972).

A visual analysis of figure 6 shows little correspondence between the two datasets. During the first part of the time-series (from season numbers 1 to 21, or years 71-72 to 92-93) there seems to be some correspondence between years with a high occurrence frequency of extreme snowfall episodes (>60 mm of 3-day precipitation in Embrun) and avalanche cycle sums. This period shows high correlation coefficients between all precipitation thresholds and avalanche activity (table 3). However, the strong increase in seasonal avalanche activity occurring from season number 34 (2005-2006) onwards (figure 6 (b)) is not reflected in an increase in extreme precipitation events, which seem to decrease slightly during that period (figure 6 (a)). This is reflected by no significant correlations at any threshold over this time period (table 3); over the entire studied period, correlations are also not significant between avalanche activity and precipitation at any level (table 3).

d a ys a b o ve t h re sh o ld su m t o ta l a va la n ch e a ct iv ity

Table 3: Correlation coefficients (R) between seasonal avalanche activity sum and seasonal count of days included in 3-day precipitation events, at three threshold levels. First and second half are shown

separately, entire period shown in third column. Significant values shown in green, non-significant values in red. All values calculated with MATLAB tool.

4.3 Return Periods

The obtained recurrence intervals for 3-day event intensities of up to 60 mm are shown in figure 7. All recurrence periods are relatively short, remaining well under a year even at 60 mm. In winter, 60 mm of precipitation roughly amounts to 60 cm of snow, depending on conditions (Ancey, 1998). Curves for different moments in time are shown in color, while the average recurrence over the 39-year period is shown in grey. A second graph showing events of up to 40 mm is provided in Appendix 8 (c), allowing for more detail regarding differences in this section.

Figure 7: Graph showing recurrence interval over 3-day event intensity. Curves for 1972 and for 2011 are shown.

Very little difference is observed between the two moments in time until event thresholds of over 40 mm, after which larger differences are witnessed. The recurrence intervals are longer in 2011 than in 1972 for event totals between 40 and 60 mm. This suggests extreme precipitation events were less frequent in 2011 than in 1972 in the Embrun valley.

corr. coeff. (R) p-val. (%) corr. coeff. (R) p-val. (%) corr. coeff. (R) p-val. (%)

30 mm 0.52 1 0.1 64 0.08 61

40 mm 0.57 1 0.15 47 0.12 42

60 mm 0.78 <0.1 -0.11 60 -0.02 87

71/72 - 92/93 93/94 - 17/18 71/72 - 17/18

4.4 Embrun in Relation to its Surroundings

A separate dataset provided by MeteoSwiss (Isotta et al., 2013) allows for a uniform altitude comparison of daily precipitation at Embrun and the average daily values for the French Alps. A graphic summary of the output is presented in figure 8: monthly precipitation in Embrun is below the region mean by 40.69 mm on average over the 2001-2008 period.

Figure 8: Monthly sums of daily precipitation in Embrun versus the mean of the French Alps. Differences between monthly sums plotted in blue. Period of 2001 to 2008. Altitude correction not necessary as corrections conducted in compilation of dataset by Isotta et al. (2013). Precipitation is lower in Embrun on a regular basis in recent times.

Daily Precipitation: Embrun v/s surrounding area 2001-2008

0 10 20 30 40 50 60 70 80 90 Time (months) -400 -300 -200 -100 0 100 200 300 400 m on th ly s u m o f d ai ly v al ue s (m m )

deviation from regional average regional average

5. Discussion

Snow avalanches are inherently a very unpredictable phenomenon. Because of the multitude of factors influencing the formation of instability in a snowpack and the randomness of triggering, every event has unique characteristics (Jamieson et al., 2008; McClung & Schaerer, 2006; Eckert et al., 2010). This renders the study of the influence of causal factors, such as heavy precipitation, very difficult, especially when the aim is to witness changes in these dynamics over time. Statistical time-series analysis of avalanche data usually requires large amounts of independent data with a high spatial variability (Eckert et al., 2013; Jones & Jamieson, 2004), while the investigation of the links between avalanches and their causes necessitate a case-based approach to ensure data accuracy (Eckert et al., 2010). Time-series analysis of avalanche events and their predictors are forced to compromise between these approaches (Jomelli et al., 2007; Hendrikx et al., 2006; Naaim et al., 2016). This part of the study offers a critical look at the analysis and its outcome and attempts to place the found results within context. A first paragraph discusses possible shortcomings of the datasets. A second section will propose an interpretation of the results while a third part will discuss the place of these results within the larger context of climate change in the French Alps. A short perspective on opportunities for further research will be provided at the end of the discussion.

5.1 Data

5.1.1. Spatial Variability in Snowpack

The usage of point data for precipitation and temperature was selected to ensure a continuous and accurate record (Jomelli et al., 2007). As outlined in the methods section, care was taken to ensure avalanche paths were used for which the Embrun weather station would provide relatively accurate representation. However, the area shows large spatial variability in precipitation (Isotta et al., 2013), certain avalanche paths receiving different amounts of snow than measured at the weather station. This variability is probably partly dependent on wind direction, with avalanche paths located on windward aspects possibly receiving more precipitation than measured at the weather station while leeward slopes might receive less snowfall (Lee & Kim, 2008).

Wind is also an important direct driver of snowpack instability and avalanching (Lehning et al., 2008) as it can transport snow in important quantities, creating supplementary deposition in leeward areas while “scraping dry” windward slopes (Jomelli et al., 2007). Wind transported snow is also more prone to slab formation, further enhancing the potential for avalanching (McClung & Schaerer, 2006). Unfortunately, no long-term instrument record of day to day average wind speeds was available for the Embrun valley, and this study was unable to include this driving factor in its analysis. It would be a valuable further addition to control for the effect of wind in extreme precipitation induced direct action avalanching.

5.1.2. EPA inaccuracy

The absence of onsite precipitation or wind records is due to the difficulty and danger of access of avalanche paths during winter: this issue is also reflected in the quality of the EPA avalanche dataset for the Embrun valley. Despite the EPA being among the best quality avalanche event time-series records available, large imprecisions remain especially in the more distant past. A report by several government organisms overseeing the EPA database warns of missing data and less dedicated event recording for the 1971-1990 period (MEDD, 2005), which might have caused bias in the analysed dataset (figure 9). The first period of the EPA data also comprises many observations with very

imprecise time records (up to an entire season interval – anything longer than 3-4 days was considered unusable for this study). The increase in observation rigor is likely to have been caused by stricter recording protocols (Garcia & Beranger, 2002; MEDD et al., 2005) but also enhanced safety equipment and recent increases in recreational winter backcountry travel (Naaim et al., 2013).

Figure 9: Total sum of avalanche activity index, plotted per season. The strong increase occurring from the early 2000’s onwards is likely to be caused by a recording bias and not by a sudden change in avalanche regime.

5.2 Interpretation of Analysis 5.2.1 Cross Correlation

The first section of the results discusses the output of the cross-correlation analysis. It finds the highest correlations between avalanche cycles and precipitation occurring two days before the event. This is strongly in line with the theory presented in the initial framework (Table 1): extreme snowfall causes severe loading of the snowpack but needs to gain inherent cohesion before forming a storm slab and obtaining potential for avalanching (McClung & Schaerer, 2006 – p.84, p.92.; Hendrikx et al., 2005): this process causes the two-day lag observed between peak precipitation and peak avalanching. Correlations of avalanche cycle activity and other driving factors remain very low, rarely exceeding the significance envelope; weak layer presence seems to correlate quite poorly, and the correlation with temperature is negative and preceding avalanching with three days which means periods prior to avalanching are colder than normal more often than abnormally warm. These results also support the theory of snowfall being an essential driver in avalanche activity around Embrun. It must be noted that the negative correlation with temperature disappears when lags tend towards zero, which means avalanche cycles, even if precipitation driven, seem to occur most often during rapid relative warming. This is also in line with the theory a short term relative warming is thought to contribute to storm slab cohesiveness increases (McClung & Schaerer, 2006 – pp.98-99).

The dominance of precipitation as an avalanche predicting factor is also shown by the avalanche / precipitation correlation curves presented in figure 5. As the number of wet snow temperature driven avalanche events is quite low, total avalanche activity correlation follows the direct-action correlation curve very closely. It is necessary to note that these outcomes might have been biased through human observations: avalanche were only classified as wet snow if specifically categorised as such in the EPA.

It might be possible that the number of wet snow avalanches is underrepresented in the database; however, this would mainly affect the correlation coefficient negatively, and meanwhile significant correlation is still found between avalanche cycle index and precipitation.

The first part of the analysis shows relatively low correlation coefficients throughout all time lags and throughout all included possible driving factors. However, these correlations achieve significance over several sections, and their variation over time lags shows a strong link between precipitation two days previous and avalanche cycles. This, in alliance with existing literature (Hendrikx et al., 2005; Eckert et al., 2010) strongly suggests snowfall is the main driver on the short-term initiation of avalanche cycles, qualifying most events as direct-action avalanches. If precipitation is the key predictor in avalanche cycle occurrence, it might entail that possible changes in precipitation regimes in the valley will cause changes in avalanching regimes.

5.2.2 Time-series

The second part of this paper’s results showed the Embrun weather station’s precipitation instrumental record and the EPA avalanche index time-series. The following paragraphs will provide a short discussion regarding these time-series, their relation to each other and their change over time. Figure 6 shows the seasonal count of days with extreme precipitation and the yearly cumulative avalanche cycle index, which represents yearly total avalanche occurrence. Appendix 6 (a) shows a daily count in both categories. According to the theoretical framework and the previous findings presented in this study, seasons with a high count of extreme precipitation days should show a high cumulative cycle index. However, this is not obvious from figure 6 (nor from Appendix 6 (a)) as there is quite a discordance between the two time-series, and this discordance seems only to grow with time as more avalanche data becomes available. A more detailed analysis using correlation coefficients (table 3) shows an interesting shift: correlations between the time-series are significant over the first half (71/72 – 91/92) of the analysed period and any correlation disappears with the increase in available avalanche data. This study attributes this shift to changes in data collection: during the 1970’s and 1980’s only major avalanches were recorded, often because of damaged or buried infrastructure (Garcia & Beranger, 2002). Yearly cumulative cycle indices would remain low unless extreme events caused very strong cycles resulting in the EPA observer to take notice. With increased observation rigor, many more avalanches are recorded, leading to generally much higher daily indices and higher cumulative indices; meanwhile techniques for recording of precipitation at the Embrun weather station remain unchanged. This “noise” does not affect the link between precipitation and avalanching, as shown in Appendix 3 (b). Nevertheless, the absence of a measure for avalanche magnitude allows small avalanches to contribute to overall cycle index to the same extent as major events. As these small avalanches are more likely to occur with low intensity precipitation events, it seems possible that the increased recording drowns out the relation between extreme precipitation event occurrence frequencies and daily or seasonal avalanche cycle indices (figure 5; table 2; Appendix 6 (b)). A more elaborate technique, perhaps using daily scaled comparisons and avalanche events weighted according to size, might prove more appropriate for the analysis of the second half of the time-series, but was unavailable for this study.

5.3 Precipitation Regimes in Embrun v/s the French Alps

Several studies asses precipitation in Europe (Alewijnse, 2004) and more specifically the French Alps (Castebrunet et al., 2012; Gaume et al., 2013) to intensify and become more clustered, resulting in more and heavier extreme snowfall events during winter time. However, the Embrun instrumental record does not seem to reflect this trend. Appendix 5 (a) shows no increase in seasonal occurrence frequency of precipitation events at any of the selected thresholds. Appendix 5 (b) considers the intensity of extreme precipitation events but doesn’t show an increase in seasonal average of extreme events. Figure 7 also shows an actual increase in recurrence interval of 3-day precipitation events exceeding 40 mm between 1972 and 2011, suggesting a decrease in extreme event frequency. Events with 3-day totals below 40 mm remained quite stable over that period (Appendix 8 (c)).

This discordance between previous literature and results might be explained by an analysis of the secondary dataset provided by MeteoSwiss. Figure 8 shows a relatively strong difference between values in Embrun and the rest of the French Alps, with Embrun values generally lower than average over the 2001-2008 period. This is also reflected in Appendix 7(b) and 7(c), with Embrun data showing little resemblance to the average behavior of the French alps, with most resemblance occurring with the minimum values in the area. Gaume et al. (2013) show fairly average precipitation behavior of the Embrun on 100-year timescales but find 30-year return levels that are slightly below the French Alps average, which somewhat reflects the outcome presented previously. Nevertheless, the time and spatial scales of consideration and analysis techniques were very different, so comparisons need to be considered carefully. A more thorough study of extreme events centered on the Embrun area in relation to the French Alps in general would be required to draw more significant conclusions regarding the behavior of Embrun precipitation and subsequent avalanching.

The Embrun weather station was selected because of its complete record, its proximity to avalanche tracks, its central location in the French Alps, and its long-term precipitation behavior being mapped as average in the area (Gaume et al., 2013). Unfortunately, a more thorough analysis of the data compiled by Isotta et al. (2013) (figure 8) seems to indicate that in fact Embrun might be a dry outlier when it concerns precipitation in the Alps. The relative drought and low extreme precipitation occurrence frequency is likely to be accentuated in part by the weather station’s low elevation (Kieffer Weisse & Bois, 2001). In addition to the somehow biased avalanche data, this prevents this study from inferring any findings from Embrun to a broader scale and offers an important reminder to the spatial variability observed in the Alps and to the danger of making spatial assumptions.

5.4 Opportunities for Further Research

Despite the difficulties encountered during the time-series analysis, the correlation between precipitation intensities and avalanche cycles remains valid. The usage of precipitation and snow cover models such as in Jomelli et al. (2007) and Castebrunet et al. (2012) could reduce discrepancies caused by spatial precipitation variability. Ever increasing monitoring of avalanche events as well as modern techniques such as remote sensing might further increase the quality of EPA data, broadening analysis possibilities in the future. Further analysis regarding precipitation/avalanche relations in other parts of the Alps would be highly relevant for the understanding of the sensibility of avalanches to climatic forcing through precipitation; it would also prove useful for more practical applications such as forecasting and hazard mapping.

6. Conclusion

The Embrun valley is regularly affected by snow avalanches during the December-April winter season. The occurrence of avalanching cycles correlates strongly with precipitation, showing the dominance of direct action type avalanches (Hendrikx et al., 2005) on the surveyed paths.

A consideration of the influence of wind on avalanche cycle occurrence would have been a valuable contribution to this study. Moreover, factors such as temperature and upper snowpack stability have a non-negligible influence on cycle occurrence, but the driving factor for avalanche occurrence is snowfall. The two-day lag accounting for slab formation, as presented in McClung & Schaerer (2006), is reflected by the Embrun data.

A strong increase in recorded avalanches is attributed to changes in backcountry frequentation and enhanced observation rigor rather than to changes in avalanche regimes. This shift is also believed to be responsible for discordance between extreme precipitation events and avalanche cycles, as the increased observation of small avalanches might have rendered the EPA record oversensitive for this study’s purposes.

Finally, the Embrun precipitation record does not show increases in extreme event frequency or intensity over the surveyed period (1971-2018); and return periods have increased between 1972 and 2011. This disagreement with existing literature (Alewijnse, 2004; Gaume et al., 2013) might be explained by the character of the precipitation regime in the Embrun area, which seems to be quite different from the average of the surrounding French Alps, at least during the years 2001 to 2008. More research focussing on extreme snowfall events in this area and surrounding areas seems necessary: although this study demonstrated a relatively simple link between heavy precipitation and avalanches, it found this relation to be much more complex when approached through a time-series, with changes in observation techniques and spatial precipitation variability playing an important role.

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8. Appendices

Appendix 1

Appendix 1: Table of selected avalanche tracks and specification of their main characteristics. Data gathered from EPA database (metadata & locational maps) and Google Earth tools.

Appendix 2

An excel sheet containing the modified EPA dataset, working, cross correlation outputs and meta data is available for download at the following link:

https://drive.google.com/open?id=1Q2WpE5HprNq_QZxiaDdaTTRWoLl_R4oi

Sector Number Index used Distance to Embrun weather station (m) Visible from the valley Average Start zone altitude Aspect

Chateauroux 28 chtx28 8195 Yes 2400 SW

Chateauroux 22 chtx22 6900 Yes 2500 E-SE

Chateauroux 21 chtx21 7500 Yes 2350 E Chateauroux 20 chtx20 7600 No 2300 N Chateauroux 19 chtx19 7800 No 2300 N Chateauroux 5 chtx05 8650 Yes 2500 E Chateauroux 6 chtx06 8700 Yes 2300 SE Chateauroux 7 chtx07 8800 Yes 2400 SE Chateauroux 18 chtx18 7800 No 2200 NE Chateauroux 26 chtx26 8900 Yes 2500 S Orcieres 6 orr06 14000 No 2350 NW Crevoux 1 crvx01 9000 Yes 2300 SW Crevoux 2 crvx02 9000 Yes 2300 SW Crevoux 4 crvx04 7800 Yes 2300 N Crevoux 5 crvx05 7700 Yes 2400 N Crevoux 6 crvx06 7000 Yes 2200 S

Embrun 2 emb2 5800 Yes 2250 SE

Embrun 3 emb3 6400 Yes 2300 SE

Embrun 5 emb5 4900 Yes 2300 E

Embrun 6 emb6 4200 Yes 2400 E-SE

Embrun 7 emb7 5100 Partial 2400 E

Puy Sanieres 1 ps1 4900 Yes 2400 S

Puy Saint Eusebes 1 pse1 6100 Yes 2400 S - SW

Saint Andre d'Embrun 1 sae01 5600 Yes 2350 W-NW

Appendix 3

Appendix 3 (a): Cross correlation for all studied influencing factors over winter season from 1971/1972 to 1990/1991 first half of studied period.

Appendix 3 (b): Cross correlation for all studied influencing factors over winter seasons from 1991/1992 to 2017/2018.

Cross correlation conducted as verification of constant behavior of factors influencing avalanche cycle occurrence. Graphs presented as an appendix as they are of secondary relevance to the main research question. The behavior over time lag as well as coefficient values remain quite close throughout time, in similar fashion as described in the first part of the Methods section. It must be noted That the maximum correlation with precipitation is slightly higher after 1991, and that temperature seems to have a stronger negative correlation with avalanches after 1991.

Appendix 4

1. Yearly Avalanche Activity TCIcumyear = [sum(TCI(30:182)),sum(TCI(183:333)),... sum(TCI(334:484)),sum(TCI((485):635)),sum(TCI(636 :786)),sum(TCI(787:937)),... sum(TCI(938:1088)),sum(TCI(1089:1239)),sum(TCI(12 40:1390)),... sum(TCI(1391:1541)),sum(TCI(1542:1691)),sum(TCI(1 692:1842)),... sum(TCI(1843:1993)),sum(TCI(1944:2144)),sum(TCI(2 145:2295)),... sum(TCI(2296:2446)),sum(TCI(2447:2597)),sum(TCI(2 598:2748)),... sum(TCI(2749:2899)),sum(TCI(2900:3050)),sum(TCI(2 051:3201)),... sum(TCI(3202:3352)),sum(TCI(3353:3503)),sum(TCI(3 654:3655)),... sum(TCI(3655:3805)),sum(TCI(3806:3956)),sum(TCI(3 957:4107)),... sum(TCI(4108:4258)),sum(TCI(4259:4409)),sum(TCI(4 410:4560)),... sum(TCI(4561:4711)),sum(TCI(4712:4862)),sum(TCI(4 863:5013)),... sum(TCI(5014:5164)),sum(TCI(5165:5315)),sum(TCI(5 316:5466)),... sum(TCI(5467:5617)),sum(TCI(5618:5768)),sum(TCI(5 769:5919)),... sum(TCI(5920:6070)),sum(TCI(6071:6221)),sum(TCI(6 222:6372)),... sum(TCI(6373:6523)),sum(TCI(6524:6674)),sum(TCI(6 675:6825)),... sum(TCI(6826:6976))];

2. Yearly sum 3-day Precipitation & Plotting against yearly Avalanche Activity

%% calculate extremes for 3 day precip limit3 = 300; % set lower limit of precip as extreme: 300, 400 or 600 * 0.1 mm occurencerecord3 =0; for i = 1:length(1) if threeprecip(i)< limit3 Precipmod3(i)=0; Datemod3(i)=0; occurencerecord3 = [occurencerecord3; 0]; else Precipmod3(i)=threeprecip(i); Datemod3(i)=Date(i); occurencerecord3 = [occurencerecord3; 1]; end end figure bar(Date, Precipmod3') extrdens = [sum(occurencerecord3(30:182)),sum(occurencerecor d3(183:333)),... sum(occurencerecord3(334:484)),sum(occurencerecor d3((485):635)),sum(occurencerecord3(636:786)),sum (occurencerecord3(787:937)),… sum(occurencerecord3(938:1088)),sum(occurencereco rd3(1089:1239)),sum(occurencerecord3(1240:1390)), ... sum(occurencerecord3(1391:1541)),sum(occurencerec ord3(1542:1691)),sum(occurencerecord3(1692:1842)) ,... sum(occurencerecord3(1843:1993)),sum(occurencerec ord3(1944:2144)),sum(occurencerecord3(2145:2295)) ,... sum(occurencerecord3(2296:2446)),sum(occurencerec ord3(2447:2597)),sum(occurencerecord3(2598:2748)) ,... sum(occurencerecord3(2749:2899)),sum(occurencerec ord3(2900:3050)),sum(occurencerecord3(2051:3201)) ,... sum(occurencerecord3(3202:3352)),sum(occurencerec ord3(3353:3503)),sum(occurencerecord3(3654:3655)) ,... sum(occurencerecord3(3655:3805)),sum(occurencerec ord3(3806:3956)),sum(occurencerecord3(3957:4107)) ,... sum(occurencerecord3(4108:4258)),sum(occurencerec ord3(4259:4409)),sum(occurencerecord3(4410:4560)) ,... sum(occurencerecord3(4561:4711)),sum(occurencerec ord3(4712:4862)),sum(occurencerecord3(4863:5013)) ,... sum(occurencerecord3(5014:5164)),sum(occurencerec ord3(5165:5315)),sum(occurencerecord3(5316:5466)) ,... sum(occurencerecord3(5467:5617)),sum(occurencerec ord3(5618:5768)),sum(occurencerecord3(5769:5919)) ,... sum(occurencerecord3(5920:6070)),sum(occurencerec ord3(6071:6221)),sum(occurencerecord3(6222:6372)) ,... sum(occurencerecord3(6373:6523)),sum(occurencerec ord3(6524:6674)),sum(occurencerecord3(6675:6825)) ,... sum(occurencerecord3(6826:6976))]; m = mean(extrdens); s = std(extrdens); figure subplot(2,1,1) bar(extrdens)

xlabel('season number (starting 71-72)') ylabel('days above threshold')

title(['Days above ' , num2str(limit3/10) ,' mm

3 day precipitation threshold per season'])

subplot(2,1,2) bar(TCIcumyear)

xlabel('season number (starting 71-72)') ylabel('sum total avalanche activity') title ('Total avalanche activity per season')

3. Final Plotting %%

figure subplot(2,1,1) bar(extrdens30)

xlabel('season number (starting 71-72)') ylabel('days above threshold')

title(['Days above 3 day precipitation threshold per season']) hold on bar(extrdens40) bar(extrdens60) hold off legend('30 mm', '40 mm', '60 mm') subplot(2,1,2) bar(TCIcumyear)

xlabel('season number (starting 71-72)') ylabel('sum total avalanche activity') title ('Total avalanche activity per season')

4.1 Correlation yearly avalanche / Extreme precipitation episodes

[Result Pval] =

corrcoef(extrdens,TCIcumyear);

Appendix 4: Matlab Scripts for analysis of Embrun & EPA data.

Appendix 5

Appendix 5 (b): Average intensity of 3-day precipitation extreme events, yearly cumulative rainfall during events above respective thresholds divided by total days of that season – not true mean but used as index for event intensity. This does not show increase over time in at the Embrun weather station. A ve ra g e p re ci p ita tio n ( *0 .1 m m )

Appendix 5 (a): Graphic

representation of seasonal count of 3-day precipitation events exceeding set thresholds. Precipitation measured at the Embrun weather station.

Appendix 6

% AVALANCHE SELECTION SECOND PART %%

limitAVI = 0.03 ; % set percentage/100 of tracks that avalanched during winter

% = a cycle intensity lower limit

lengthAVI = size(selectInd); %length of avalanche record

eventrecAVI = zeros(lengthAVI); %initialise record % dynamic selection for k = 1:lengthAVI(1) if TCI(k) < limitAVI eventrecAVI(k) =0; else eventrecAVI(k) = 1; end end TotalAVI = sum(eventrecAVI) selectInd = eventrecAVI .* TCI;

Appendix 6 (a): MATLAB script for avalanche selection according to cycle intensity.

Appendix 6 (b): (a) Seasonal count of days included in a 3-day precipitation event exceeding thresholds as given in figure legend. (b) Seasonal count of days included in 3-day avalanche cycle event exceeding thresholds as given in figure legend Seasons are shown on x axis depending on first studied season (dec.1971 - april 1972).

d a ys a b o ve t h re sh o ld d a ys a b o ve t h re sh o ld

Appendix 7

%% INITIALISE close all clear all clc

%% set comparison level lowerlong = 6; upperlong = 8; lowerlat = 43; upperlat = 45; %% Initialise values meanmonthRec = 0 ; anommonthRec = 0; valmonthRec = 0; minmonthRec = 0; maxmonthRec = 0; j = 20010100 %% load data ncdisp('RapdD_al05.etrs.laea_20010100.nc'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% %% DYNAMIC PART while j < 20081200 % initialise values meanday = 0; meandayRec = 0; anom = 0; anomRec = 0; valRec = 0; mindayRec =0; maxdayRec = 0; %load values %a = ncread('RapdD_al05.etrs.laea_20010100.nc','PRECIP ITATION');

a = ncread(['RapdD_al05.etrs.laea_' num2str(j) '.nc'],'PRECIPITATION');

%% find embrun area

lat = ncread('coord_lonlat.nc','Latitude'); long = ncread('coord_lonlat.nc','Longitude'); longselect = ( lowerlong < long & long < upperlong);

latselect = ( lowerlat < lat & lat < upperlat); longlatselect = longselect .*latselect; [Xselect,Yselect] = find (longlatselect); %% find Embrun EmbrX = 153; EmbrY = 35; %% %% calculation for i = 1:28 meanday = mean(a([min(Xselect), max(Xselect)],[min(Yselect), max(Yselect)],i)) ; valRec = [valRec; a(EmbrX, EmbrY,i)];

meandayRec = [meandayRec; meanday(2)]; anom = a( EmbrX, EmbrY,i) - meanday; anomRec = [anomRec; anom(2)]; minday = min(a([min(Xselect),

max(Xselect)],[min(Yselect), max(Yselect)],i)) ; mindayRec = [mindayRec, minday(2)];

maxday = max(a([min(Xselect),

max(Xselect)],[min(Yselect), max(Yselect)],i)) ; maxdayRec = [maxdayRec; maxday(2)];

end valmonth = sum(valRec(2:end)); meanmonth = sum(meandayRec(2:end)); anommonth = sum(anomRec(2:end)); minmonth = sum(mindayRec(2:end)); maxmonth = mean(maxdayRec(2:end)); valmonthRec = [valmonthRec; valmonth]; meanmonthRec = [meanmonthRec;meanmonth]; anommonthRec = [anommonthRec; anommonth]; minmonthRec = [minmonthRec; minmonth]; maxmonthRec = [maxmonthRec; maxmonth];

if j == 20011200 j = 20020100 else if j == 20021200 j = 20030100 else if j == 20031200 j=20040100 else if j== 20041200 j= 20050100 else if j== 20051200 j= 20060100 else if j == 20061200 j= 20070100 else if j == 20071200 j= 20080100 else j = j+100; end end end end end end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% %% viualisation figure bar(anommonthRec)

title('Deviation of Embrun weather station v/s

Surrounding 2001-2008')

ylabel('mm from mean') xlabel('time (months)') ylim([-20 20] ) hold on

plot(meanmonthRec, 'r') plot(valmonthRec, 'g')

legend('Deviation from mean', 'Mean of Area', 'Measured in Embrun')

%le('Deviation of Embrun daily Precip v/s entire area')

figure

plot (meanmonthRec, 'r')

title('Precipiatation Embrun weather station v/s

Surrounding 2001-2008')

ylabel('average of daily values (mm)') xlabel('time (months)')

hold on

plot (valmonthRec, 'm') plot(minmonthRec, 'y') plot(maxmonthRec, 'b')

legend('area mean','Embrun value', 'area minimum', 'area maximum')

%% correlation

[C1,P1] = corrcoef(valmonthRec, meanmonthRec) [C2,P2] = corrcoef(valmonthRec, minmonthRec) [C3,P3] = corrcoef(valmonthRec, maxmonthRec)

Appendix 7(a): MATLAB Script for analysis of MeteoSwiss data, dataset compiled by Isotta et al. (2013). Area selected for comparison 2 degrees of longitude and 2 degrees of latitude, or 163 by 222 km.

Appendix 7(b): Monthly averages of daily precipitation values of Embrun grid cell and monthly average of daily spatial mean as well as minimum and maximum value for the region of the French Alps. Period of 2001 to 2008. Values obtained from MeteoSwiss dataset compiled by Isotta et al. (2013). Embrun bears little resemblance to plotted average and mean / max.

Appendix 7(c): Correlation Coefficients between time-series of monthly averages of Embrun grid cell daily values and daily spatial average as well as daily min and max. There is very little resemblance between Embrun values and other time-series, but a comparison at extreme events would be more relevant. a ve ra g e o f d a ily v a lu e s (m m )

Min French Alps Max French Alps

Daily Value Embrun Mean French Alps -0.085

-0.1189 0.0644 corr. coeff.