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EVALUATING THE EXPOSURE OF HELISKIING SKI GUIDES TO AVALANCHE
TERRAIN USING A FUZZY LOGIC AVALANCHE SUSCEPTIBILITY MODEL
Andrew Eirik Ainer Sharp
University of Leeds, School of Geography
A dissertation presented in partial fulfillment of the requirements for the degree
MASTER OF SCIENCE
GEOGRAPHIC INFORMATION SYSTEMS
June, 2018
2
Table of Contents
List of Tables ....................................................................................................................... 5
List of Figures ..................................................................................................................... 6
Abstract ............................................................................................................................... 8
Introduction ....................................................................................................................... 10
Background ....................................................................................................................... 12
Characteristics of Snow avalanches .............................................................................. 12
Definitions and classifications .................................................................................. 13
The mechanics of avalanche release ......................................................................... 14
Terrain factors affecting avalanche susceptibility: .................................................... 15
Avalanche hazard: ..................................................................................................... 17
Applications for GIS ..................................................................................................... 18
Geomorphology ........................................................................................................ 18
Spatial analysis .......................................................................................................... 19
Spatial modelling of natural hazards ......................................................................... 19
Literature Review .............................................................................................................. 20
The use of GPS tracks to explore the risk management practices of guides ................ 20
Potential avalanche release area modeling ................................................................... 23
Parametrization of avalanche terrain ........................................................................ 23
Multi-Criteria Analysis and the modeling of Natural Hazards ................................. 30
Evaluation and validation of natural hazard models ................................................. 34
3
Threshold selection ................................................................................................... 38
Research Objectives .......................................................................................................... 40
Data Summary .................................................................................................................. 41
Study Area ..................................................................................................................... 41
Data acquisition and pre-processing ............................................................................. 43
Digital elevation data ................................................................................................ 43
Forest cover data ....................................................................................................... 44
GPS Tracks ............................................................................................................... 44
Avalanche start zone inventory ................................................................................. 45
Additional data .......................................................................................................... 47
Preprocessing of data: ............................................................................................... 47
Methodology ..................................................................................................................... 47
Avalanche susceptibility and potential release are modeling ....................................... 47
Spatial Analysis ............................................................................................................. 54
Results ............................................................................................................................... 55
Potential Release Area model ....................................................................................... 55
Exposure of GPS Tracks to Potential Release Areas .................................................... 59
Discussion ......................................................................................................................... 65
PRA model performance ............................................................................................... 65
Relationship between hazard and exposure to potential release areas .......................... 68
Future research. ............................................................................................................. 70
4
Conclusion ........................................................................................................................ 71
References ......................................................................................................................... 72
APPENDIX A ................................................................................................................... 82
5
List of Tables
Table 1: Classifications of avalanche size .................................................................................... 14
Table 2: Canadian Avalanche Hazard Rating Scale (Canadian Avalanche Association, 2016) .... 17
Table 3: Primary and secondary morphometric parameters ......................................................... 19
Table 4: Approaches to the idenification of potential release areas. ............................................. 23
Table 5: Confusion matrix for the evaluation of binary classification schemes ........................... 35
Table 6: geospatial data used to provide visal content and reference ........................................... 47
Table 7: Cauchy membership function parmaterization ............................................................... 52
Table 8: Pearson correlation ion coefficient between the parameter membership functions and the
PRA class membership ................................................................................................................. 58
Table 9: Performance comparison of binary PRA classifier and binary slope-based classifier .... 59
Table 10: Summary of GPS track segments with PRA polygons ................................................. 61
Table 11: PRA class membership values extracted from GPS tracks by hazard rating ................ 63
Table 12: Ordinal linear regression of the 90th quantile of PRA class membership and hazard
rating. ............................................................................................................................................ 64
6
List of Figures
Figure 1 Slope angle in the starting zone of human triggered avalanches (N =809, 1st quantile:
37o, median: 39o, 3rd quantile: 41o) from Schweizer and Jamieson (2001) .................................. 16
Figure 2: Example of S calculation for three cells of interest along a directional vector from
(Winstral et al., 2002) ................................................................................................................... 26
Figure 3: Calculations of the vector dispersion measure of terrain ruggedness using
neighborhood analysis of vectors orthogonal to each grid cell from Sappington et al. (2007) .... 27
Figure 4: scale effects on geomorphological parametrization from Deng et al. (2007). .............. 29
Figure 5: Threshold independent validation and evaluation of natural hazard models from
Begueria (2006).(a) Sampling, (b) model construction, (c) model validation and (d) model
evaluation. ..................................................................................................................................... 36
Figure 6: Threshold selection approaches form a ROC curve ...................................................... 39
Figure 7: CMH Galena Operational Overview ............................................................................. 43
Figure 8: Data sample for the Magic Fingers ski run area ............................................................ 46
Figure 9: PRA Algorithm .............................................................................................................. 48
Figure 10: PRA algorithm parameters for the Magic Fingers ski run area ................................... 49
Figure 11: Cauchy membership functions for PRA class parameters ........................................... 53
Figure 12: Distribution of PRA membership for slope gradient across the study area ................. 55
Figure 13: Distribution of PRA membership for wind shelter index across the study area .......... 56
Figure 14: Distribution of PRA membership for vector roughness across the study area ............ 56
Figure 15: Distribution of PRA membership for forest stem density across the study area ......... 57
Figure 16: Distribution of PRA class membership ....................................................................... 57
Figure 17: ROC plot of the updated PRA class membership (left) and ROC Plot of Veitinger et
al’s (2016) initial implementation PRA class membership (right) ................................................ 58
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Figure 18: Fuzzy logic PRA classification with a membership threshold of 0.06 (left), binary
slope-based classification (right) .................................................................................................. 59
Figure 19: GPS track intersecting PRAs at various hazard ratings in the Magic Fingers area. .... 60
Figure 20: distribution of hazard for GPS track intersections with PRAs .................................... 62
Figure 21: Violin plot of PRA class membership values extracted from GPS tracks by hazard
rating ............................................................................................................................................. 63
Figure 22: Ordinal linear regression of PRA class membership and hazard rating over a range of
quantile values .............................................................................................................................. 64
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Abstract
Snow avalanches are the greatest risk to personal safety faced by commercial heliskiing
groups. Guides manage the risk to their groups by traveling in terrain with a low likelihood of
avalanching based on an evaluation of avalanche hazard. However, slopes with terrain
characteristics capable of producing avalanches are often the most attractive for skiing. Guides
therefore strive to balance avoiding avalanche prone slopes with the need to provide an enjoyable
skiing experience for clients. They make frequent and critical risk management decisions each
time they encounter a slope capable of producing an avalanche. There is increasing interest in
developing a better quantitative understanding of terrain-based risk management process of
professional guides with the goal of developing evidence-based decision aids. In order to better
understand the magnitude of the risk management tasks of heli-skiing guides, this study aims to
quantify the frequency of guides’ exposure to start-zones capable of producing an avalanche
large enough to bury or kill a skier and explore how guides reduce their exposure to avalanche
prone terrain as hazard increases. For this study, the methodology builds on known techniques
employed by industry for the use of GPS tracking devices in the evaluation of the avalanche risk
management expertise of ski guides, those promoted by Hendrikx et al. (2013, 2013) and
Thumlert and Haegeli (2016, 2018). It also extends Veitinger et al.’s (2016) approach for the
automated identification of potential avalanche release areas through the addition of a forest
density parameter to improve its performance in forested terrain. Lead guides at Canadian
Mountain Holidays (CMH) Galena Lodge were equipped with GPS units during the 2015 to
2018 winter seasons, creating a dataset of 6051 tracked heliskiing descents. A model of regional
avalanche susceptibility for CMH Galena’s operating tenure was developed using a fuzzy logic
analysis of morphological terrain parameters (slope gradient, ground roughness, exposure to the
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prevailing wind) derived from an 0.75 arcsecond resolution digital elevation model, combined
with forest density data. CMH guides provided a dataset of 100 documented avalanche location
polygons that were used to validate the avalanche susceptibility model and derive a threshold
criterion to identify potential release areas from a Receiver Operating Characteristics curve. The
potential release areas identified by the model were filtered based on their area and combined
with the GPS tracks using a spatial overlay analysis to explore the terrain choices of guides with
respect to avalanche susceptibility. The results of this analysis confirm that guides reduce the
frequency of exposure to potential avalanche release areas and use terrain that is less susceptible
to avalanches with these areas as avalanche hazard increases. The methodology employed
presents a novel application for the automated detection of potential avalanche release areas and
reaffirms the value in studying the terrain usage of through the analysis of GPS tracks to better
understand their management strategies.
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EVALUATING THE EXPOSURE OF HELISKIING SKI GUIDES TO AVALANCHE
TERRAIN USING A FUZZY LOGIC AVALANCHE SUSCEPTIBILITY MODEL
Introduction
The commercial helicopter skiing industry is an iconic mainstay of British Columbia’s
adventure tourism industry, providing significant economic benefits to the provincial economy
(Norrie and Murphy, 2016). Between 2013 and 2015, 14 heliskiing operations in British
Columbia attracted an average of 18,500 skiers each year. The sector provides employment to
more than 2,000 people, mainly in rural communities, and contributes an estimated $95.3M to
provincial Gross Domestic Product. Commercial heliskiing involves groups of skiers that are
transported by helicopter to predetermined landing sites. Guides then lead the group as they
descend on skis through alpine glaciers, open bowls, and forested glades. Snow avalanches are
the greatest risk threatening commercial heliskiing groups (Walcher, 2017). Between 1996 and
2014, 26 people died in avalanche accidents while heli-skiing in British Columbia (BC Coroners
Service, 2014). Guides manage the exposure to avalanche risk primarily by selecting terrain with
a low likelihood of avalanching. However, slopes with terrain characteristics capable of
producing avalanches are often the most attractive for skiing. Guides balance the risk of
exposing their groups to avalanche terrain against the need to provide an enjoyable ski
experience. In order to do so, guides make critical risk management decisions each time they
encounter a terrain capable of producing avalanches. This study aims to quantify the exposure of
heliskiing guides at Canadian Mountain Holiday’s (CMH) Galena Lodge to potential avalanche
release areas.
Heliskiing guides minimize the potential for themselves of one of their clients to trigger
an avalanche through a process of hazard avoidance. Guides continuously gather environmental
observations, which they use to assess the avalanche hazard. Recent avalanches on similar slopes
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are the strongest indicator off avalanche hazard but observations of snowpack structure and
current weather also influence their decisions. Guides then manage the risk of triggering an
avalanche by selecting terrain with a low likelihood of avalanching based on their expert
evaluation of current conditions (The Association of Canadian Mountain Guides, 2003).
Heliskiing guides may make numerous such terrain choices on each run and typically rely on
using on intuitive decision-making practices based on experience-based knowledge (Stewart-
Patterson, 2008; Stewart-Patterson, 2015).
The primary aim of this thesis is to explore the relationship between avalanche hazard
and exposure of heliskiing guides to the terrain capable of producing avalanches large enough to
bury or kill a person. A secondary aim of this thesis is to assess the opportunities and limitations
for the application of modern approaches to the identification of potential avalanche release areas
to regional scale analysis data readily available in Canada. The research serves several purposes:
• To better understand how of heliskiing guides manage avalanche risk through terrain
selection.
• To inform the development of a potential tools for effectively transferring institutional
and operational knowledge between guides within a heliskiing organization.
• With careful consideration to the future definition of metrics, this method also
presents a potential opportunity for internal and or external auditing by the operations
themselves, or outside third parties.
Several recent studies have used Geographic Information Systems to combine
geomorphological parameters and high resolution GPS tracks of guided heliskiing descents to try
and capture the terrain preferences of heliskiing guides (Hendrikx et al., 2015; Sterchi et al.,
2016; Hendrikx and Johnson, 2016; Thumlert and Haegeli, 2018). This study employs similar
techniques to explore the spatial relationship of a set of GPS tracks recorded at Canadian
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Mountain Holidays (CMH) Galena Heliskiing Lodge between 2015 and 2018 with an avalanche
susceptibility model of the operational tenure. This model of avalanche susceptibility builds on
the algorithm for the automated identification of potential avalanche release areas proposed by
Veitinger et al. (2016).
Background
Characteristics of Snow avalanches
Snow avalanches involve the rapid motion of snow down a hill or mountainside. They are
the most common mountain slope hazard to threaten people, facilities and the environment in
Canada (Stethem et al., 2003). Although avalanches can occur on any slope of sufficient gradient
given the right conditions, the potential for triggering an avalanche varies over time and space.
The likelihood of avalanche release depends on several parameters, commonly decoupled into
three classes (McClung and Schaerer, 2006):
• Terrain parameters such as slope gradient, aspect, curvature, ground roughness and
vegetative cover
• Meteorological parameters such as wind, temperature and precipitation;
• Snowpack structure parameters such as the distribution of snow crystals into distinct
snowpack layers, the strength of the bond between these layers and the existence of
the weak layers necessary for avalanche formation.
While the propensity of terrain to avalanche does not change over time, the meteorological and
snowpack conditions do vary, resulting in fluctuations in avalanche hazard. Given conditions
conducive to avalanche release, a trigger is required for avalanche formation. These triggers are
commonly in the form of increase in load such as humans on the slope, additional snow or rain,
or an explosive force; or by abrupt changes to the snow pack structure due to rain or rapid
warming.
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Definitions and classifications
Snow avalanches may be characterized by features such as their dimensions, the manner
of triggering and the dynamics of their flow downslope. Avalanche paths delineate the
geographic boundaries of known or potential avalanche terrain. They are commonly classified
according to the morphological characteristics of three zones identified within the path
(UNESCO, 1981)
• The start zone is where an avalanche is triggered and where a mass of snow becomes
unstable and starts to flow down slope.
• The track is where an avalanche reaches its maximum velocity and destructive
potential.
• The runout zone is area where the avalanche decelerates rapidly and stops.
There are two main types of avalanches, which are classified according to the mechanics of
initiation:
• Loose snow avalanches start from a point at or near the surface and entrain mass as
they flow down slope, often assuming a fan like shape.
• Slab avalanche initiation involves the mechanical failure of a weak layer buried in the
snowpack resulting in the simultaneous release of a cohesive mass of snow.
In Canada, avalanches are further classified by their size according to a logarithmic scale ranging
from 1 to 5 that takes into account estimations of their mass, path length, impact pressure and
destructive potential (Table 1).
Size
class
Destructive potential
Typical
mass
Typical
path length
Typical
impact
pressure
1
Relatively harmless to people.
<10 T
10m
1kpa
2
Could bury, injure, or kill a person.
102 T
100m
10kpa
14
3
Could bury and destroy a car, damage a
truck, destroy a wood-frame house or break
a few trees.
103 T
1,000m
100kpa
4
Could destroy a railway car, large truck,
several buildings or a forest area of
approximately 4 hectares.
104 T
2,000m
500kpa
5
Largest snow avalanche known. Could
destroy a village or a forest area of
approximately 40 hectares.
105 T
3,000m
1,000kpa
Table 1: Classifications of avalanche size
Avalanche terrain may also be described in terms of the frequency it is affected by
avalanche events. Avalanche return periods can range from several times per year to as low as
once per 300 years. Avalanche frequency is commonly corelated to the relative size of avalanche
events within the larger geographic extent of the avalanche path (McClung and Schaerer, 2006).
Smaller avalanches that release only a portion of the start zone and terminate high in the path are
more frequent than events that encompass the entire start zone and run far into the runout zone.
The mechanics of avalanche release
The morphology of the start zone, the structural properties of the snowpack and its spatial
continuity, and the current meteorological conditions control the mechanical processes that drive
the release of avalanches (McClung and Schaerer, 2006). Sheer stress is induced through the
snowpack by the gravitational effect of snow lying on a slope. Shear strength results from the
micro scale bonds between snow crystals and may vary through the snowpack depending on its
structure. Avalanche initiation requires that the sheer force on the snowpack equals or exceeds its
shear strength causing a mechanical failure (Schweizer, 1999). This failure in the snowpack can
result either from the introduction of an external load such as additional precipitation or a skier’s
weight, or the weakening of the snowpack driven by meteorological conditions (Nairz et al.,
2015). It is estimated that in approximately 92 percent of avalanche accidents, the avalanche is
triggered by the victim or someone in the victim’s party (McClung and Schaerer, 2006). These
human triggered avalanches happen by choice, not chance. This study focuses principally on
15
slab avalanches, which are responsible for the majority of fatal avalanche accidents triggered by
skiers (Pfeifer, 2009). Here, the addition of load to the snow pack causes shear fracture along a
plane of weakness in the snowpack, which propagates outwards allowing a cohesive mass of
snow to release downslope (Herwijnen and B.Jamieson, 2007). The size of the release depends
on the properties of the snowpack and the continuity of topography across the area.
Terrain factors affecting avalanche susceptibility:
Terrain is an essential factor influencing avalanche release mechanics and the only factor
that is constant over time. Avalanche susceptibility refers to the propensity for avalanches to
occur in a specific area. The concept of avalanche susceptibility relies on the fact that avalanches
tend to occur in terrain with certain morphological characteristics more frequently than others.
Statistical analysis of past events demonstrates that slope gradient is the most important factors
influencing avalanche release (Perla, 1977; Schweizer and Lütschg, 2001; McClung, 2001;
Schweizer, 2003; Vontobel et al., 2013). The physical explanation for this is that gradient
determines the component of the gravitational force experienced through the snowpack as shear
stress. In terrain with slopes below 30°, the shear stress is relatively low, and avalanches are rare.
In terrain with slopes greater than 55°, slab avalanches are unlikely since the higher shear stress
causes frequent small loose-snow avalanches that limit the accumulation of snow into cohesive
slabs on these steep slopes. Schweizer and Jamieson (2001) found that for human triggered
avalanches in Switzerland and Canada, the start zone had a median slope angle of 39°(Figure 1).
16
Figure 1 Slope angle in the starting zone of human triggered avalanches (N =809, 1st quantile: 37o, median: 39o, 3rd quantile:
41o) from Schweizer and Jamieson (2001)
While the maximum size of an avalanche start zone is theoretically unlimited, slab
avalanches require a continuous plane of weakness within the snowpack, (Habermann et al.,
2008). Mountain snow cover is generally characterized by a degree high spatial variability over a
wide range of scales, from millimeters to kilometers (Blöschl, 1999; Plattner et al., 2004).
Furthermore, snowpack distribution and terrain are not independent but rather exert a mutual
influence upon each other. Terrain affects the spatial distribution of the snow cover and
properties of the snowpack, while irregular snow distribution alters surface morphology in snow
covered winter terrain (Veitinger et al., 2014). Wind is the primary influencing process for snow
redistribution in alpine terrain (Raderschall et al., 2008). Wind–terrain interactions are therefore
a critical factor in explaining the location of slab avalanches. Avalanches occur more frequently
in lee terrain where the cumulative redistribution of snow may smooth out ground roughness that
could limit the propagation of failures thin the snowpack. (Meister, 1989; Winstral et al., 2002).
Forest cover also influences the propensity of slopes to avalanche. Trees can provide
mechanical support to the snowpack, and the interception, retention and release of snow in the
tree canopy can hinder weak layer formation (McClung, 2001). Furthermore, wind re-
distribution of snow is largely inhibited in dense forest stands (Gelfan et al., 2004). The literature
identifies numerous secondary characteristics that affect an area’s propensity to produce
()
J. Schweizer, J.B. Jamieson rCold Regions Science and Technology 33 2001 207–221212
Fig. 1. Slope angle in starting zone of human triggered avalanches.
Swiss-reported, investigated and Canadian-investigated cases are
Ž
shown jointly Ns809, 1st quartile: 378, median: 398,3rdquar-
.
tile: 418.
with the adjacent layers. First, we describe some of
the snowpack and failure characteristics in general.
Due to the distinct differences in climate, the
median snow depth in the investigated cases in
Switzerland was 1.2 m and in Canada more than
Ž.
twice as much: 2.8 m Table 2 .
In 35 out of the 95 Swiss investigated avalanches
Ž.
37% , the slab consisted of storm snow, i.e. the
failure was within the storm snow or between the
storm snow and the old snowpack. In the Canadian
data, the portion of storm snow avalanches is higher:
52%. For 45 out of the 91 Canadian cases, the age of
the weak layer, i.e. the time since it was buried, was
recorded. The median age is 11 days, the middle
50% ranged from 6 to 14 days, and the oldest weak
layer was 56 days old when it was triggered by a
skier. For the cases when the slab consisted of storm
snow, the median age was 5 days, compared to 12.5
days for the 32 cases when the failure occurred in
the old snow.
The failure was characterized as interface failure
in 51% of the investigated Swiss cases, whereas the
corresponding Canadian portion was 33%. In all
other cases, there was a distinct thin weak layer
found. For some of the weak layers, the failure could
even be assigned to one of the layer boundaries. This
would actually increase the interface failures, in fact
Ž.
to 58% in the case of the Swiss data set. Fohn 1993
¨
reported about 60% of interface failures in his analy-
sis of 300 snow profiles.
Fig. 2. Rutschblock scores of RB tests adjacent to human trig-
gered slab avalanches. Swiss and Canadian cases shown together
Ž.
Ns106 .
In most cases, a rutschblock test was performed.
The median rutschblock score in both data sets is 3
Ž.Ž.
weighting Table 2 . There is no significant differ-
ence between the two samples. Accordingly, the
frequency distribution is given for the combined data
Ž.
sets Fig. 2 . In 76% of the cases, an RB score of 2,
3 or 4 was found.
4.5. Slab properties
The median slab thickness is 52 cm in the Swiss
Ž
and 41 cm in the Canadian investigated cases Table
.Ž
2 . The two samples are significantly different ps
.
0.03 but with medians sufficiently close so that in
Fig. 3 the slab thickness is shown for the combined
data. As can be clearly seen in Fig. 3, in the majority
Fig. 3. Slab thickness of investigated avalanches. Swiss and
Ž.
Canadian cases shown jointly Ns186 .
17
avalanches, including the absolute elevation of a starting zone, its aspect, its proximity to ridges
or high points, its curvature in profile and plan, the roughness of the underlying terrain, and its
degree of forest cover (Schweizer, 2003).
Avalanche hazard:
Avalanche hazard refers to the potential for avalanches to cause damage or harm to
something of value (Canadian Avalanche Association, 2016). Avalanche hazard is a function of
the likelihood of an avalanche occurring relative to its destructive potential or size. It implies the
potential to affect people, facilities or things but does not incorporate the vulnerability or
exposure to avalanches of any particular element at risk (Statham et al., 2010). In Canada,
avalanche hazard is rated on an ordinal scale from 1 to 5. Statham et al. (2018) recently
described the general components of the avalanche hazard assessment process and arranged them
into a conceptual model for avalanche hazard; this framework has become widely adopted in the
Canadian avalanche safety community.
Hazard
Level
Likelihood of Triggering
Size and Distribution
5
Natural and artificially
triggered avalanches almost
certain.
> Size 3 avalanches are widespread
4
Natural avalanche likely;
artificially triggered avalanches
very likely.
Size 2-3 avalanches re widespread; or > size 3
avalanche in specific areas
3
Natural avalanches possible
artificially triggered avalanches
likely.
< Size 2 avalanches are widespread; or size 2-3
avalanches in specific areas; or > size 3
avalanches in isolated areas.
2
Natural avalanche unlikely;
artificially triggered avalanches
possible.
< Size 2 avalanches is specific areas or size 2-3
avalanches in isolated areas.
1
Natural and artificially
triggered avalanches unlikely.
< Size 2 avalanche in isolate areas or extreme
terrain.
Table 2: Canadian Avalanche Hazard Rating Scale (Canadian Avalanche Association, 2016)
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Applications for GIS
Geographic Information Systems (GIS) describe real world phenomena in terms of their
geographical positioning, properties and spatial interrelations. Using GIS to geographically
represent reality is predicated on using spatial data models that represent spatial variation in
either raster or vector data structures (Goodchild, 1992). GIS also provide a suite of tools that
allow for the efficient storage, manipulation, integration and visualization of a variety of spatial
data.
Geomorphology
Geomorphometry involves the quantitative analysis of land surface parameters. GIS is
widely used to derive morphometric parameters of terrain from digital elevation models (DEMs);
representations of sampled elevation information stored in a raster data structure. The
fundamental operations in geomorphometry use neighborhood operations to extract continuous
land surface parameters form a DEM. Primary parameters are calculated from the first and
second order derivatives of a local fitted surface around a grid cell of interest. These parameters
include measures of elevation, slope, curvature and terrain roughness (Table 3). With additional
processing GIS can also be used to derive secondary parameters that often coincide with
conceptions of landscape features such and mountain ranges, ridges, valleys and catchment areas
(Hutchinson and Gallant, 2000).
Terrain
Attribute
Description
Elevation (Z)
Slope
(gradient)
The maximum change in elevation over the distance between the cell and its
eight neighbors (Burrough, 1986).
Slope
(aspect)
Azimuth of the direction of maximum slope.
Curvature
Combination of plan and profile curvature (Zevenbergen and Thorne, 1987).
Plan
curvature
Curvature of the slope profile along lines of constant elevation (contour)
neighborhood.
Profile
curvature
Curvature of the slope profile perpendicular to line of constant elevation
(contour).
19
Roughness
Terrain roughness may be defined differently depending on the calculation.
This study employs the vector ruggedness measure developed (Sappington et
al., 2007)
Table 3: Primary and secondary morphometric parameters
Since potential avalanche release areas commonly described in terms of landform characteristics,
the ability to derive relevant geomorphometric parameters from digital elevation data makes GIS
highly relevant to studies of avalanche terrain.
Spatial analysis
GIS can also be used to integrate data and explore topological relationships (inclusion,
intersection, etc.) as well as the geographic characteristics (size, locations) of spatial data. GIS
can eliminate the difficult and tediousness task of making complex geographical calculations,
such as measurements of distance, area, and circumference. GIS is also useful for exploring the
statistical relationships of compositional elements. Many different types of statistical models are
used in natural hazard modelling including: classification based, tree-based, or regression
models. Classification models are particularly well suited for the analysis of discrete target
variables, such as the definition of potential avalanche release areas (Hengl and MacMillan,
2009). In particular, multi-criteria analysis provides a collection of techniques for the analysis of
geographic phenomena where the results of the analysis depend on the spatial arrangements of
the elements (Eastman, 1999). Uncertainty and imprecision can be accounted for in this analysis
through the implementation of fuzzy logic processes. Depending on the classification rules,
either a continuous or a discrete output may be produced. Furthermore, GIS enables these spatial
analysis processes to be automated using geoprocessing frameworks and tools.
Spatial modelling of natural hazards
GIS has a vital role in modeling, analyzing, predicting, and mapping avalanche terrain as
part of efforts to mitigate avalanche risk. The practice of avalanche mapping has a well-known
and widely applied methodology for avalanche risk management (Canadian Avalanche
20
Association, 2002) and GIS has been commonly used in the creation of avalanche path locator,
and risk zoning maps. Traditional approaches to avalanche mapping have relied on the principle
of precedence: that avalanches will occur again in the future in areas where the geo-
environmental conditions led to avalanches in the past. As such, the creation of avalanche maps
has traditionally relied on historical avalanche records and field investigations conducted by
avalanche experts to guide the identification of potential avalanche terrain for the assessment of
hazard zoning. However, the increasing availability of high quality digital elevation models,
combined with new approaches to the modeling and mapping of landscapes in GIS has enabled
the assessment of avalanche terrain for large or remote areas where field studies may not be
practical, or where sufficiently detailed historical records may not be available.
One such alternative approach is the analysis and mapping of avalanche susceptibility.
Several spatial distribution models requiring limited input parameters have been proposed for
regional scale analysis or in areas with limited historical records (Maggioni, 2005; Barbolini et
al., 2011; Pistocchi and Notarnicola, 2013; Bühler et al., 2013; Veitinger, 2015). These
approaches use geomorphological parameters to identify terrain with a propensity for avalanche
release. Avalanche susceptibility may be mapped as a continuous surface, which indicates where
avalanches are expected to be more or less frequent, or as discrete regions that are classified by
whether the terrain has the potential to produce avalanches or not.
Literature Review
The use of GPS tracks to explore the risk management practices of guides
Guides manage avalanche risk by first assessing the nature, severity and spatial
distribution of the local hazard, then carefully choosing terrain to mitigate that hazard (Haegeli
and Atkins, 2010). There is increasing interest in developing a better quantitative understanding
21
of terrain-based risk management process of professional guides with the goal of developing
evidence-based decision aids. Several recent studies have devloped techniques for the use of
GPS tracking devices in exploring the terrain preferences of ski guides proffesional ski guides. A
central question of interest to these studies is the what constitutes suitable terrain under different
avalanche conditions?
Hendrikx et al.(2015) explored the travel behavior and patterns of terrain usage of
heliskiing guides using data from handheld GPS units. GPS tracks and associated demographics
were collected from guides at Majestic Heli-Skiing in Alaska over a period of 18 days. The
average slope and aspect of each run were extracted from the GPS tracks and summarized as
terrain metrics. These parameters were then used to explore variations in the terrain preferences
between guides operating under similar conditions through a non-parametric Kruskal-Wallis test.
The study found only a weak correlation avalanche hazard and the slope angles skied. However,
it demonstrated the potential of studying GPS tracks to quantify the terrain selection preferences
of guides.
Haegeli and Atkins (2016) identified that the Hendrikx et al.’s (2015) limited results may
have been due to an overly simplified perspective on heli-skiing operations. They proposed a
structured recording and data collection methodology to comprehensively cover the terrain
choice and risk management proccesses of professional ski guides. They developed a
comprehensive geodatabase system and a series of R packages (Haegeli et al., in prep.) to
process raw GPS files and store the extracted tracks and supportive operational information in a
postgreSQL data base that would allow researchers to interact with the data. GPS tracks were
captured from guides at CMH Galena over a winter season and used explore the habitual pattres
of how indiviual runs are skied. The study found that guides follow an anchoring and ajdustment
22
heuristic in their selection of terrain. Habitual patterns of movments are combeind with targeted
adjustments in repsonce to particular avalanch hazard conditions and operational needs.
Thumlert and Haegeli (2018) explored the terrain selection decisions of professional
guides to produce a classification of avalanche terrain ‘severity’. Following the methodology
developed by Haegeli and Atkins (2016), guides at Mike Wiegele heliskiing in British Columbia
were equipped with passive GPS trackers over two winter seasons. Four terrain parameters
(slope, vegetation, downslope curvature and cross slope curvature) were extracted for a region
buffered along each track. These parameters were then considered as in dependent variables in a
mixed effect ordered regression model of avalanche hazard. The study found that the guides
skied steeper, less densely forested, and more convoluted terrain during periods of lower
avalanche hazard. The analysis lead to the production of a set of maps that identified terrain the
guides deemed acceptable for skiing as the avalanche conditions improved.
Several benefits to this line of research have been identified. The long-term collection of
terrain usage data at a heliskiing operation allows for the exploration and evaluation of the risk
management process and expertise of guides. This can provide a useful operational tool for self-
check-ins, the transfer of institutional knowledge with a guiding team, or external auditing.
Thumlert and Haegeli (2018) also been proposed that by isolating the relationship between
avalanche hazard and terrain selection, it may be possible to capture and quantify the expertise of
professional guides into meaningful evidence-based terrain guidance tools for managing risk in
avalanche terrain. However, to date all of these studies have decouple the morphological
parameters affecting the avalanche susceptibility of terrain. Modern potential release area
algorithms developed for avalanche risk assessment contexts attempt to rate avalanche terrain
according its propensity to avalanche. These models pose an interesting opportunity for a new
terrain metric to be applied to the study of guides patters of terrain usage.
23
Potential avalanche release area modeling
Several algorithms have been proposed (Table 4) that attempt to identity potential
avalanche release areas through the spatial analysis of geomorphological parameters.
Authors
Terrain Parameters
DEM Resolution
Classification
Approach
(Barbolini et al.,
2011)
Slope, plan curvature
10m
Binary
(Bühler et al., 2013)
Slope, plan curvature,
roughness
5m
Binary
(Chueca Cía et al.,
2014)
Slope, plan curvature
5m
Binary
(Ghinoi and Chung,
2005)
Slope aspect,
elevation, curvature
distance to ridge
20m
Continuous
(Maggioni and
Gruber, 2003)
Slope aspect, plan
curvature, distance to
ridge
25m, 50m for
curvature
Binary
(Yilmaz, 2016)
Slope, aspect,
elevation, plane
curvature, profile
curvature, vegetation
density
10m
Continuous
(Veitinger et al.,
2016)
Slope, wind shelter,
roughness
2m
Continuous
Table 4: Approaches to the idenification of potential release areas.
Parametrization of avalanche terrain
Avalanches tend to occur in terrain that is continuous, appropriately steep, sheltered to the
prevailing winds, and either open or not too densely forested. The primary parameter in all these
studies is local slope gradient. Additional parameters that have been used to try and capture
terrain heterogeneity and wind-terrain effect include curvature, terrain roughness, wind shelter
indices and topographic landform identification. To date, no studies have considered the
influence of forest cover other than using it as a masking variable to exclude forested terrain
from analysis. Parameters are combined through a multi criteria analysis using either a Binary,
weighted linear average or fuzzy logic approach to produce either a binary classification system
identifying potential avalanche release areas or a continuous avalanche susceptibility index.
24
Geomorphometric parameters
All of these approaches to the identification of potential avalanche release areas rely on
the geomorphometric parameterization of avalanche terrain from a digital elevation model
(DEM). Terrain parameters can be calculated from first and second-order derivatives of a locally
fitted surface around a grid cell of interest. One widely adopted method for approximating the
characterization of surfaces is the use of bi-quadratic polynomials of the form:
!"#$%&'%($'%)$%*'%+ ,-.
where z corresponds to the elevation estimate at a point (x, y) and a through f are the coefficients
that define the quadratic surface(Evans, 1972).
Gradient
Slope gradient is the primary terrain factor affecting a particular slope’s propensity to
release avalanches. To calculate slope gradient using quadratic parametrisation as proposed by
Wood (1996), the magnitude (slope) of the steepest gradient at the central grid cell of the fitted
surface needs to be determined. To derive this, the rate of change in x and y direction is
calculated as follows:
/0
/12"
345
/0
/1
6
7%
5
/0
/2
6
7
8
,9.
where:
)!
)$"9&'%($%*
,
:
.
)!
)$"9&'%($%*
,
;
.
such that:
)!
)$'"
<
)7%*7
,
=
.
Slope
>
and aspect
?
are thus:
>"@#ABC
<
)7%*7
,
D
.
25
?E"@#ABC*
)
,
F
.
Slope gradient is expressed as integral degrees or integral percentage measured from
horizontal. Aspect is expressed in integral cardinal degrees, measured clockwise from 0o at true
north.
Wind-terrain effects
A slope’s aspect relative to the prevailing wind as another parameter affecting terrain’s
propensity to avalanche. In this case, aspect refers to a slope’s tendency to align on the windward
or lee side of a terrain break. Various parameters have been proposed to model terrain-wind
effects. (Maggioni, 2005) proposed that concave areas are more prone to avalanche formation
than convex areas due to wind deposition favouring gullies and down slope terrain steepening.
Elevation and distance to ridge lines have also been proposed as important parameters affecting
wind deposition (Gauer, 2001). However, neither of these parameters allow for wind-terrain
effects to account for the influence of wind direction. Plattner et al. (2004) proposed a wind
shelter parameter to capture snow accumulation patterns in high elevation alpine terrain relative
to a prevailing wind direction. This approach takes into the account the maximum gradient
within the upwind portion of a circular neighbourhood a measure of topographic wind sheltering
(Winstral et al., 2002):
O
CTOBER
2002 529WINSTRAL ET AL.
F
IG
. 4. Example of Sx calculations for three cells of interest along
a2708search vector. As depicted, with dmax set equal to 300 m, the
shelter-defining pixel for cells 1 and 2 is cell A, producing positive
Sx values. The shelter-defining cell for cell 3 is cell B, producing a
negative Sx. Had dmax been equal to 100 m, the search for the shelter-
defining pixel for cell 1 would not extend across the valley, thus
producing a negative Sx for cell 1, while Sx for cell 2 would remain
the same and that for cell 3 would be slightly lower.
Sx determinations are provided in Fig. 4. Theoretically,
increasingly negative Sx values correspond to greater
constrictions on the approaching wind flow, leading to
increasing wind speeds, while increasingly positive Sx
values correspond to larger and more proximal land-
scape obstacles, producing a greater degree of shelter
and lower wind speeds. Values of Sx were determined
along vectors at 58increments within the upwind win-
dow and averaged to formulate the mean maximum up-
wind slope parameter, , defined bySx
A2
1
A2
Sx (x,y)| 5Sx (x,y), (2)
O
dmax iiA A,dmax ii
1
n
A5A
y
1
where n
y
is the number of search vectors in the window
defined by A
1
,A
2
, and dmax. Search distances of 50 m
(
50
), 100 m (
100
), 300 m (
300
), 500 m (
500
),Sx Sx Sx Sx
1000 m (
1000
), and 2000 m (
2000
) were used to testSx Sx
the influence of near and far terrain.
It was felt that calculated for within-basin sitesSx
would have been only slightly affected by the 10-m
DEM’s restricted view of the western topography, given
the considerable western obstruction presented by the
Continental Divide. Hence, was calculated from theSx
10-m DEM.
The Sb parameter was designed to delineate topo-
graphic features capable of generating flow separation.
To obtain Sb, independent representations of near and
far topographic features were necessar y. The difference
between relative slope measures of the local and out-
lying topography supplied a measure of the break in
upwind slope. To determine Sb, two applications of the
Sx algorithm were used to determine a local Sx (Sx
1
)
and an outlying Sx (Sx
o
) A user-defined separation dis-
tance (sepdist) determined the cutoff between the two
regional Sx calculations, with Sx was determined along
an upwind search vector with a maximum search dis-
tance (dmax) equal to the separation distance (sepdist)
to determine Sx
1
, defined as
Sx (x,y)5Sx (x,y).
1ii A,sepdist ii
A
(3)
The distant or outlaying terrain described by Sx
0
was
defined as the Sx
A,1000
of the cell located the separation
distance upwind of the cell of interest along each re-
spective search vector:
Sx (x,y)5Sx (x,y),
oii A,1000 oo
A
(4)
where [(x
o
2x
i
)
2
1(y
o
2y
i
)
2
]
0.5
˘sepdist and (x
o
,y
o
)
∈(x
y
,y
y
). Subtraction of Sx
o
from Sx
1
yielded Sb. The
average of each vector calculation of Sb within the up-
wind window formed a mean measure of upwind slope
break, , defined bySb
A2
Sb (x,y)|
sepdist iiA
1
A2
1
5[Sx (x,y)2Sx (x,y)]. (5)
O
1ii oii
AA
n
A5A
y
1
In order to determine Sx
o
for many pixels located near
the Continental Divide it was necessary to analyze ter-
rain beyond the western extent of the 10-m DEM. There-
fore, Sx
o
was determined from the 30-m DEM, while
calculation of Sx
1
remained at the 10-m scale to retain
high-resolution depictions of proximal topography.
In addition, Sx
o
was used to measure the relative up-
wind exposure of each potential slope break. With Sb
providing a means of locating cells downwind of con-
siderable slope breaks,
o
[calculated from Eq. (2) withSx
Sx
o
substituted for Sx] was independently evaluated to
determine whether the described slope break was subject
to the high winds and assumed correspondent high
snow-transport fluxes needed to produce substantial
downwind drifts. Based on threshold values of andSb
o
, a drift delineator variable (D
0
) was establishedSx
whereby each sample was classified as either being with-
in or outside of a modeled lee-slope drift zone. Applied
in this manner, D
0
was a first approximation that broadly
defined drift areas; intradrift accumulation differences
were not explicitly represented.
b. Data analysis
We sought to quantify how these redistribution pa-
rameters ( and D
0
) related to measured snow depthsSx
in two ways. First, we sought to answer the question,
‘‘Are and D
0
significant predictors of snow depth?’’Sx
while also examining the best length scales to use for
calculating and D
0
. Linear regression and analysisSx
of variance (ANOVA) were used to perform the afore-
mentioned analyses. Second, we asked the question,
‘‘What effects do the addition of and D
0
have on aSx
multivariate model of snow distribution?’’ In response
to this latter question, regression tree modeling was used
to formulate and compare two tree models of snow dis-
26
Figure 2: Example of S calculation for three cells of interest along a directional vector from (Winstral et al., 2002)
GA)*$
,
H
.
"@#ABC
3
I#$
JK
!
,
$L
.
M!
,
$
.N
O
$LM$
O
PQ$RH
S8,
T
.
where
H"H
,
$LP#PU#P)
.is a subset of raster cells within a distance
)
and range in
direction
#VU#
from the central cell
$L
. Vei tinger et al. (2016) implemented this function as a
parameter for modeling avalanche susceptibility but replaced the max function with a third
quantile function account for the fact that in high resolution DEMs very large sheltering effects
may be outweighed if the surrounding area is open to wind influence. This wind shelter index
varies between -1.5 and 1.5 in complex alpine terrain, with negative values corresponding to
wind-exposed terrain and positive values corresponding to wind sheltered terrain.
Surface continuity and roughness
“Rugged terrain” has been described as topographically discontinous, broken, or rough.
Rugged terrain can inhibit the formation of continuous weak layers in the snowpack and/or
provide mechanical anchoring to the snowpack, inhibiting avalanche release. Various paramtertes
include variations in the slope, plane and profile curvature, and terrain roughness, each of which
have been proposed in the literature to model the terrain continuity characteristic of avalanche
release areas. In these models the ideal measure of terrain ruggedness needs to detect changes in
slope, while minimizing its direct dependence on slope, since slope is typically already
27
incorporated as a primary parameter.
Figure 3: Calculations of the vector dispersion measure of terrain ruggedness using neighborhood analysis of vectors orthogonal
to each grid cell from Sappington et al. (2007)
Bühler et al. (2013) advocated the vector dispersion measure of vector ruggedness
definition (Sappington et al., 2007) for avalanche susceptibility analysis. This measure of terrain
ruggedness uses a three-dimensional dispersion of normal vectors to the modeled planar facts of
a landscape. The variability of the vector orientations over a given measurement extent serves as
the measure of the irregularity of the topographical surface (Figure 3). The measure is
independent of slope but can distinguish changes in both slope and aspect. The normal unit
vectors for every grid cell of a DEM are decomposed into orthogonal components. A resultant
vector |r| is then obtained for every pixel by summing up the single components of the centre
pixel and its neighbours. The neighbourhood size is defined by the number of pixels n taken into
account:
,
$P'P!
.
"
,
WGA>X(YW?PWGA>XWGA?P(YW>P
. ,
Z
.
28
O
[
O
"
\5]
$
6
7%
5]
'
6
7%
5]
!
6
7
,
-^
.
The vector ruggedness measure R:
_"-M
O
[
O
A
,
--
.
is a measure of the surface roughness with values ranging from 0 (flat) to 1 (extremely
rough).
Effects of scale
Terrain parameters derived from gridded elevation models depend inherently on scale
(Goodchild, 1992). For raster data models, scale incorporates two components: the measurement
resolution (the grid dimensions of the DEM), and the measurement extent (the window size over
which a terrain parameter is calculated) (Figure 4). DEM resolution influences the output of
potential release area identification algorithms. At courser scales, land surface features such as
smaller ridges and gullies that are highly relevant for small avalanches may be overlooked.
Macro scale studies of the morphological features of entire avalanche paths that have determined
DEM resolutions of 30 meters or greater are unable to describe surface terrain adequately for the
identification of features relating to avalanche susceptibility (McCollister et al., 2003). While
DEMs with resolutions of up to 25mhave been used in avalanche release area models in the past,
terrain capable of producing smaller avalanches can being overlooked when DEMs with
resolutions of greater than 10m are employed (Dreier and Bühler, 2014). However, the benefits
of finer resolution DEMs are limited as smaller scale terrain features may be hidden by the
smoothing effects of the winter snowpack and therefore are not relevant for the analysis of
avalanche terrain.
29
Figure 4: scale effects on geomorphological parametrization from Deng et al. (2007).
The measurement extent also has an effect in Evans’ (1972) original approach to the six
unknown parameters (a through f in Equation 1), each of which were defined to take into account
all the grid values within a 3×3 neighbourhood around the central cell. Wood (1996) expanded
this concept by fitting the quadratic surface over any arbitrarily sized window, allowing for
parameters to be calculated over a varying measurement extent. Goodchild and Quattrochi
(1997) identified that morphological features may or may not be present when measuring a
property at different scales. Maggioni and Gruber (2003) were the first to propose that different
scales may be appropriate to different parameters with respect to avalanche release area
identification. Computed terrain variables such as elevation, slope, aspect, plane and profile
curvature vary significantly with changes in the grid cell size of a raster DEM (Kienzle, 2004).
Since the scale of a DEM is often arbitrarily defined, it may not necessarily be related to the
scale of characterization required, meaning that the derived results may not always be
representative. Veitinger et al. (2016) suggested that the inclusion of other morphological
parameters in identification algorithms may not offer a significant improvement over a slope-
only based classification for larger resolution DEMs. However, by varying the extent of the
window size, a surface parameter can be calculated at varying scales without changing the
30
resolution of the elevation model. Veitinger et al. (2014) showed that varying the measurement
extent in the calculation of terrain parameters can be useful for capturing the progressive
smoothing of terrain roughness by a mature winter snowpack and that resampling high resolution
DEMs can improve the performance of automated avalanche release area detection algorithms.
Forest cover parameters
Forest cover can inhibit the formation of continuous week layers and can also provide
mechanical anchoring to the snowpack (Brang et al., 2008). Previous attempts to model
avalanche susceptibility have considered forest cover as a masking variable used to exclude
forested terrain from the analysis. Viglietti et al.(2010) and Teich et al.(2012) proposed an
empirical principle describing the properties of evergreen forests necessary to hinder medium to
large avalanche release. Avalanche release is in unlikely in forests with a regular distribution and
a canopy cover greater than 50-60%. For forests with a canopy cover of less than 50%, the
protection effect depends on the density of live and dead tree stems, typically measured in stems
per hectare. Gaps between trees of larger than 30 m (~11 stems/ha) along a slope cannot hinder
avalanche release, avalanches less likely in forests with gaps between stems of about 15m or less
(~44 stems/ha). Avalanches are not expected in forests with spacing of 5m or less (~450 stem/ha)
(McClung, 2001). This relationship has not been exploited in any avalanche susceptibility
models to date.
Multi-Criteria Analysis and the modeling of Natural Hazards
The majority of avalanche susceptibility models identify potential avalanche release
using a multi-criteria evaluation used either a binary intersection also known as a Binary
approach, a weighted linear combination approach, or a fuzzy logic approach.
31
Boolean classifications
In the Boolean approach, binary classification layers are created for each attribute seen as
a constraint. Multiple layers may be then combined through an intersection analysis where only
areas that satisfy all the constraints appear in the final model. A Binary approach to avalanche
susceptibility based on slope may define as any slope with a gradient of less than 25o or greater
than 55o as not being susceptible to avalanches and assign them a classification value of 0 while
slopes with a gradient between 25o and 55o are assigned a classification value of 1. The resulting
layer would identify all the terrain steep enough to produce an avalanche. Such approaches are
able to distinguish between areas were avalanche can and cannot release but are unable to
identify potential release areas that may be more susceptible to avalanching that others.
Weighted linear combinations
Weighted linear combinations (Eastman, 1999) are able to account for such varying
degrees of susceptibility. In this approach weights are assigned to each attribute considered as a
criterion. Weights may be defined through expert assessment, or a regression analysis. Each
parameter is them molded as a continuous range of values that defined the scaled value of that
attribute to its alternative. Continuing from the previous example, the slope parameter may be
assigned a range of values defined by:
`
,
a
.
"
b
c
d
c
e
^f ag^
aM9=
9^ f9=hai;^
==Ma
9^ f;^hai==
^f aj==
,
-9
.
The resulting continuous criteria are then combined as a weighted average. The total
score is calculated by multiplying the weight assigned to each attribute by its scaled value. The
resulting model captures variations in susceptibility missing in the Boolean approach, however,
natural process can be rarely can described by models that result from such sharply defined
parameterizations.
32
Fuzzy logic approaches
Fuzzy logic has been proposed as an approach that is able to better capture the significant
degrees of uncertainty and vagueness arising out of the complex nature of modelling the process
and the parameters involved. A challenge in identifying “continuous steep and wind sheltered
terrine is that it is difficult to precisely define what steep or wind sheltered terrain actually is.
Zadeh (1965) proposed the fuzzy logic approach as an alternative to classical logic, better able
deal with such imprecise datasets and diffuse rules. The fuzzy logic method allows for more
flexible combinations than weighted linear combinations and overcomes the limitations of
sharply defined parameters through the concept of membership functions where each parameter
is assigned a degree of membership in a particular class. Formally this is expressed as;
“Let
k
be a space of points (objects), with a generic element of
k
denoted by
l
. Thus,
kE"El
. A fuzzy set (class)
m
in
k
is characterised by a membership (characteristic)
function
no,l.
which associates with each point in
k
a real number in the interval
p^P-q
,
with the value of
no,l.
at x representing the ”grade of membership” of
l
in
m
”. (Zadeh,
1965)
Fuzzy Operators
Fuzzy set theory is supported by a strict mathematical framework. Zadeh (1965)
originally defined three basic operators: union (OR), intersection (AND) the complement
(negation).
+rst,$.E"EI#$p+u,$.P+v,$.qP$EREw
,
-:
.
+rxt,$.E"EIGAp+u,$.P+v,$.qP$EREw
,
-;
.
+yr,$.E"E-M+u,$.P$EREw
,
-=
.
These operators are non-compensatory in the sense that a low value of one fuzzy set
cannot be compensated by high value in another. However, this approach may be inadequate for
33
modeling when conflicting variables are aggregated (Zimmermann ,1987). The fuzzy OR and
fuzzy AND operators proposed by Yager( 1988) allow for compensation between variables:
+rst
,
$
.
"EzE{I#$
p
+r
,
$
.
P+t
,
$
.q
%
,
-Mz
.K
+r
,
$
.
%+t
,
$
.N
9P$EREwPzEREp^P-q
,
-D
.
+rxt
,
$
.
"Ez{IGA
p
+r
,
$
.
P+t
,
$
.q
%
,
-Mz
.K
+r
,
$
.
%+t
,
$
.N
9P$EREwPzEREp^P-q
,
-F
.
These operators make it possible to define the desired level of compensation between variables.
When
z"-
these operators correspond to the classical intersection operator. However, for
z"
^E
these operators correspond to the arithmetic mean. Defining:
z"-MEIGA
p
+r
,
$
.
P+t
,
$
.
P|
q ,
-T
.
For the union operator this allows the level of compensation to be inversely proportional to the
minimum membership value of the parameters under consideration. When the membership
values for all parameters is high the operator behaves like the arithmetic mean. However, when
the membership value for one or more of the values is the operator behaves like the classic
union.
This behavior can be illustrated by a practical example: Under a minimum intersection
operator terrain that is sufficiently steep (
}~
,
$
.
"^•=
) and located in open forested terrain
(
}€
,
$
.
"^•=
) would have the same susceptibility index as terrain that is sufficiently steep but in
a more open glade (
}€
,
$
.
"^•T
). An expert assessment, however, would likely classify the
open terrain as more susceptible to avalanches. The partial compensation of the fuzzy logic
intersection allows for this. If on the other hand the gradient of the open slope was insufficiently
steep
}~
,
$
.
"^•-
while the angle of the forested terrain remained sufficiently steep for
avalanche formation
}~
,
$
.
"^•=
, then the fuzzy intersection operator would reduce
compensation and resemble a minimum intersection. This is appropriate since nearly lower angle
terrain will rarely avalanche even if it is open.
34
Fuzzy membership functions
Several approaches to the definition of fuzzy membership functions have been proposed
in the literature. Membership may be derived from empirical models of physical attributes
(Veitinger et al., 2016), through a frequency ratio approach (Lee, 2007; Kumar et al., 2016), or
through analytical hierarchy process (Nefeslioglu et al., 2013). Membership values may also be
based or modified upon subjective judgement (Bonham-Carter, 1994). Simple and
computationally efficient membership functions such as triangular or trapezoidal functions,
generalized bell functions (also referred to as Cauchy membership function) or Gaussian
functions are preferred (Jang et al., 1997). Cauchy functions may offer increased flexibility
compared to other approaches. They are typically characterized by smooth curves where the
sharpness of transition can be stipulated by parametrization of the function:
}
,
$
.
"-
-%
5
$M(
#
6
7•
,
-Z
.
The literature of natural hazards modelling considers fuzzy logic modelling approaches
as generally superior over binary classifications and weighted linear combinations. This is
particularly evident in the context of applications where the underlying physical processes are
not fully understood and where empirical relations and assumptions need to be exploited.
Evaluation and validation of natural hazard models
Model validation is a fundamental step in any natural hazards study that involves an
evaluation of the predictive power of a model. Validation imparts confidence in a model and is of
great importance for transferring the results to the final users. In the field of natural hazards,
model validation may involve assessment of the model’s sensitivity to parametrisation through
Monte Carlo Simulations, comparisons of the model output with other model results, or
operative validations that compare model output with a database of past observed events
(Caswell, 1976; Rykiel, 1996). Comparing simulated values with measured data is desirable
35
when such data exists. However, many natural hazard occurrences including avalanches are
infrequently measured accurately, and so it may be necessary to validate these models against
either a small sample size of measured occurrences, or the subjective assessment of experts.
Confusion matrix
Different validation techniques may be applied depending on the type of model output.
Binary classification schemes of avalanche susceptibility produce only two classes of data: areas
where avalanche can occur, and where they cannot occur. The classification output of these
models is then compared to the actual observations obtained from reference data. Four different
outcomes are possible in a binary classification model, commonly expressed through a confusion
matrix (Stehman, 1997).
Observation
Prediction
Positive
Negative
Positive
True Positive (TP)
False Positives (FP)
Negative
False Negatives (FN)
True Negatives (TN)
Table 5: Confusion matrix for the evaluation of binary classification schemes
Model performance statistics can be calculated from this matrix:
‚[*(GWGYAE" Eƒ‚E
ƒ‚E%„‚
,
9^
.
Eu((…[#('E"E ƒ‚E%ƒ†
ƒ‚E%ƒ†E%„‚E%„†
,
9-
.
H*AWG@G‡G@'E"E ƒ‚
ƒ‚E%„†"WˆE
,
99
.
H‰*(G+G(G@'E"E ƒ†E
ƒ†E%„‚"WŠ
,
9:
.
These statistics require some interpretation in the context of modeling natural hazards
such as avalanche occurrences. Accuracy measures alone may be insufficient in terms of
evaluating the quality of a model a where the hazard only affects a small proportion of the whole
study area. In such cases, measures of model sensitivity (Equation 22) and specificity (Equation
23) which take into account the distribution of both the observed and predicted classes should
36
also be provided. Furthermore, when comparing model results to historical data, false positive
results should not automatically be considered as classification errors. Since avalanche
occurrences are relatively rare, false positive results could also represent areas where avalanches
have not been observed but may occur in the future.
Receiver operating characteristic
For continuous model output the use of the confusion matrix requires the definition of a
threshold to split the continuous index into two classification classes. The selection of this is
often subjective and is typically not a characteristic of the model itself but a result of the use of
the model in a specific context. Thus, it is desirable in validating continuous classification
indices to assess the predictive power of the model independent of thresholds (Figure 5)
(Begueria, 2006). Once the model has been validated, appropriate classification thresholds are
selected, and accuracy statistics are generated for resulting binary classifier.
Figure 5: Threshold independent validation and evaluation of natural hazard models from Begueria (2006).(a) Sampling, (b)
model construction, (c) model validation and (d) model evaluation.
The Receiver Operating Characteristic (ROC) approach has been employed in previous
studies (Lee, 2007; Brenning, 2008; Bühler et al., 2013; Kumar et al., 2016; Yilmaz, 2016) to
assess the performance of continuous index classification models for natural hazards against a
data set of previously observed events. ROC graphs plot the true positive rate (sensitivity)
Chapter 2. State of the art 38
Figure 2.16: Threshold independent validation and evaluationof natural hazard mo d-
els from Beguera (2006). (a) Sampling, (b) model construction, (c) model validation
and (d) model evaluation.
37
against the false positive rate (1- specificity). A ROC graph depicts relative tradeoffs between
benefits (true positives) and costs (false positives) and have the attractive property of being
insensitive to changes in class distribution. The ROC curve is the interpolated curve made
of points whose coordinates are functions of the threshold
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A discrete classifier produces only a single point in ROC space. Classifiers appearing on
the left side of a ROC graph, near the X axis, may be thought of as ‘conservative’; they make
positive classifications only with strong evidence resulting in few false positive errors, however
such conservativism often comes at cost of reduced model sensitivity. Conversely, classifiers on
the upper right-hand side of the ROC graph may be thought of as ‘liberal’: they make positive
classifications with weak evidence, so they classify nearly all positives correctly, but this often
comes at the cost of model specificity. The diagonal line
'"$
represents the performance of a
random guess classifier. Any classifier that appears below this line performs worse than a
random classification.
ROC curves can also be used to compare classifier performance against other model
results. This is accomplished by comparing the area under the ROC curve (AUROC). This takes
a value between 0.5 (no discrimination) to 1.0 (perfect discrimination) that can can serve as a
global accuracy statistic for the model (Begueri, 2006). A disadvantage of this is approach is that
AUROC comparison can give potentially misleading results if the ROC curves of two classifiers
cross, in which case subjective interpretation of the curves in the context of the model
application may be required.
38
Threshold selection
Continuous classification models produce a continuous numeric index that represents the
degree to which an instance is a member of a class. Depending on the formulation of the attribute
membership functions these values can be strict probabilities, in which case they adhere to
standard theorems of probability; or they can be general, uncalibrated scores, in which case the
only property that holds is that a higher score indicates a higher probability. Many practical
applications of these models require that the discrete classification sets be generated from the
class membership index through the application of a threshold criteria.
The problem of threshold selection falls into the frame work of supervised classification.
In such problems the aim is to construct a decision rule that assigns new objects into one of a
prespecified set of classes, using descriptive information about those objects. The rule is
constructed from a ‘training set’ of data which consists of descriptive information for a sample of
objects for which one also knows the true class labels. Many approaches to constructing such
classification rules have been explored in the literature, including: tree classifiers, neural
networks, and nearest neighbour methods. Classifier selection from the analysis of ROC curves
have been widely adopted in the context of fuzzy logic natural hazard models where the selection
of an appropriate threshold depends on the context of application and the costs classification
errors rather than on the characteristics of the model itself. Thresholds may be selected from the
ROC curve that maximize true positive rate, minimize the false positive rate, or both.
A common approach is to consider a threshold as having better performance than another
if it’s is classifier in ROC space is closer to upper right corner of the plot (Fawcett, 2006). For
distance
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39
then the optimal threshold will the ROC point for which
)
is minimum. This threshold balances
maximizing the true positive rate while minimizing the false negative rate. However, in the case
of natural hazard models validated against an incomplete data set, the priority may not be
minimizing false negatives since false positive results could also represent areas where a hazard
has not been observed but may occur in the future. Conversely the cost of false negatives may
high since the hazard may only affects a small proportion of whole study area.
An alternative approach is to select a threshold that provides the largest improvement in
model specificity over a random guess. The Youden index is the point on the ROC curve farthest
from line of equality (x=y).
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The Max Youden index selects a threshold that maximised difference between the true positive
rate and false negative rates. This is commonly referred to as the informed-ness of the model,
however, this approach risks producing threshold that is overly conservative.
Figure 6: Threshold selection approaches form a ROC curve
40
Research Objectives
This study aims to test two hypotheses:
• Guides reduce the frequency of their exposure to terrain capable of producing
avalanches large enough to bury or kill a person as avalanche hazard increases.
• Guides choose terrain that is less susceptible to avalanches as avalanche hazard
increases.
Answering these questions requires addressing several research tasks. First, the study
explores the opportunities and limitations for the application of modern potential release area
algorithms for regional scale analysis of avalanche susceptibility using data readily available in
Canada. The study adapts the fuzzy logic algorithm for the identification of potential avalanche
release area proposed by Veitinger et al (2016) for a regional scale analysis of the avalanche
susceptibility. These adaptations include:
• Replacing the algorithm’s Boolean forest cover mask with a fuzzy forest cover
parameter based on the empirical relationship between forest density and avalanche
susceptibility identified by Teich et al. (2012)
• Updating the algorithm’s fuzzy slope membership function to better reflect the
distribution of slope in records of human triggered avalanche accident (Schweizer and
Lutsc, 2001).
The model will be implemented for the CMH Galena operational tenure. A dataset
capturing an expert assessment of terrain capable of producing avalanches large enough to bury
or kill a person will be used to validate the model and select a classification threshold to identify
potential avalanche release areas. Secondly, the study will explore the spatial relationship
between both the regional scale model the avalanche susceptibility and the binary classification
41
model of potential avalanche release areas with the guides terrain usage at different levels of
avalanche hazard, captured in a dataset of GPS tracks of guided ski descents.
Data Summary
Study Area
The study region is the Canadian Mountain Holidays (CMH) Galena Lodge Heliskiing
tenure, a 1,166 km2 region in the Selkirk Mountains of British Columbia, Canada (Figure 7). The
rugged topography consists of glaciated mountain peaks that rise up to 3060m, giving way to
broad forested valleys with a maximum vertical relief of 2,610 m. The tenure’s terrain tenure is
classified into three main elevation bands: below tree line, tree line and alpine. These
classifications are important as CMH Galena rates avalanche hazard for each band separately.
Operational records show that tenure can receive upwards of 10m of annual snowfall and is
exposed to prevailing south-westly winds.
The Galena tenure is broken down into 300 ski runs in which skiing operations are
typically confined. Each run has a predefined helicopter landing zone and pick up location.
However, there are multiple options for descent routes that a guide may choose to follow when
descending from the landing to the pickup. CMH Galena operates a Bell 212 helicopter that can
service four groups of 11, and a Bell 407 helicopter that can service two groups of five. Each
skier group is led by one guide. The lead guide generally has many years of experience and is
highly familiar with the operating tenure. They are serviced first by the helicopter on each run
and are responsible for choosing which run will be skied, although subsequent groups may elect
to ski different route variations down a particular run.
The guides use a systematic framework to evaluate avalanche hazard and choose terrain
as part of their overall individual risk management process. Avalanche hazard is assessed each
morning as group, based on a synthesis of weather, snowpack, and previous avalanche
42
occurrence data. An estimation of the likelihood and spatial distribution of potential avalanches
is combined with a prediction of the potential avalanche size to produce a daily avalanche hazard
forecast for each of the three elevation bands. This hazard rating informs the development of the
day’s operational plan and run list, a document of runs open to skiing operations for the day. The
list is composed of runs where the guiding team collectively agrees avalanche risk can be
managed to appropriate levels by route selection. After the skiing operations have concluded for
the day, the guides reconvene to debrief and report weather, snowpack and avalanche occurrence
observations; the hazard ratings for each elevation band are then updated to reflect this new data.
Whereas the moorings hazard assessment is a forecast of avalanche conditions expected, the end
of day assessment represents a nowcast of conditions experienced in the field. This process is an
operational fixture of all commercial ski guiding operations in Canada and is described in more
detail in Statham et al. (2010), Haegeli et al.( 2014), and Haegeli and Atkins (2016).
43
Figure 7: CMH Galena Operational Overview
Data acquisition and pre-processing
Digital elevation data
This study employs only readily available data for the modeling of avalanche
susceptibility. A coverage mosaic of raster digital elevation data was acquired from the Canadian
Digital Elevation Model (CDEM) dataset through Natural Resources Canada Geogratis. The
data’s horizontal reference is in the North American Datum 1983 (NAD83) with a resolution of
44
0.75 arc second. Elevations are expressed as integers in reference to mean sea level (Canadian
Geodetic Vertical Datum 1928 (CGVD28)) and measured in meters. CDEM elevations for the
region are recorded as ground elevations. Quality control assures that the CDEM data is smooth
within the grid and continuous from one elevation point to the next, except at natural break
points such as streams, cliffs, and craters. Drainage anomalies have been eliminated. Measured
accuracy is 15 to 20 m (Canada, 2013).
Forest cover data
Forest cover data for the study region was obtained from the British Columbia Vegetation
Resources Inventory (VRI) (Ministry of Forests, Lands and Natural Resource Operations, 2015)
vector dataset through DataBC. The VRI is a photo-based inventory detailing both where a
vegetative resource is located and how much of a given vegetation type is within an inventory
unit. This study employed the VRI Live Stems per Hectare and VRI Dead Stems per Hectare
attributes. This dataset describes the number of living and dead trees visible to the photo
interpreter in the dominant, codominant and high intermediate crown positions for each tree layer
in each inventory. It is expressed as stems per hectare. Life stem and dead stem data was added
for each polygon and a stems-per-hectare raster was generated from VRI polygons in ESRI
arcGIS.
GPS Tracks
Lead Guides at CMH Galena were equipped with passive GPS tracking units during the
2015/16, 2016/17, 2017/18 winter seasons. The custom-designed passive trackers were set to
record positional data every four seconds which resulted in an average distance between
observation points of 20 m while skiing. The technological specification of this system are
described in Haegeli and Atkins (2010). The GPS units generated a comprehensive dataset
composed of 6651 ski descents over the three seasons. The point location observations of
45
identified runs were then combined into spatial line geometries and stored in the PostgreSQL
database (Thumlert and Haegeli, 2018). The sarp R packages (Haegeli et al., in prep.) were used
to process the GPS files and store the extracted run tracks as linear geometries. The GPS tracks
were broken down into 14,395 segments based on each track’s intersection with the three
elevation bands (alpine, tree line, below tree line). CMH stores operational data on InfoEx, a
compressed database system described in Haegeli et al.(2014). The daily record of end of day
(PM) avalanche hazard assessment was extracted from this database and joined as an attribute to
the GPS tracks. Hazard ratings were not recorded for the 2018 winter season. To ensure the
dataset only included ‘successful’ terrain choices, the data was filtered for avalanche
involvements. GPS tracks recorded on days with skier accidently triggered avalanche incidents
of size 2 or larger would have been excluded from the dataset. However, no such incidents
occurred during the study period.
Avalanche start zone inventory
A survey of CMH Galena’s senior guides was used to generate a vector data set
representing terrain with the potential to produce avalanches large enough to burry or kill a
person. Fourteen ski runs were selected by the guides as areas that represented a broad range of
terrain types present in the tenure covering the three elevation bands. The runs selected were
those in which the guides were confident in their ability to precisely identify terrain features of
concern. These areas were manually discretized as polygon features from satellite imagery in
Google Earth. It is important to note that these polygons do not represent a complete dataset of
all the terrain capable of producing avalanches; but only a sample terrain features that have
produced avalanches in the past. This dataset represents examples terrain features where natural
or human triggered avalanches large enough to burry or kill a person had occurred in the past.
The avalanche conditions under which these prior avalanche events had occurred was not
46
recorded since avalanche susceptibility should isolated terrain from meteorological or snowpack
factors. These avalanche release areas were imported into ArcGIS as a vector polygon feature
class and then converted to a binary classification raster.
Figure 8: Data sample for the Magic Fingers ski run area
47
Additional data
Other datasets were used to add enhanced visual content and to provide visual reference
during the generation of the validation dataset are listed in Table 6. These datasets were not used
in any analytical processes
Dataset
Source
Description
Terrain Resource Information Management
Representational Data
Data BC
1:20,000 Vector base
map data
Digital Globe World Imagery
ESRI
0.5m resolution satellite
imagery
Table 6: geospatial data used to provide visal content and reference
Preprocessing of data:
All datasets were projected to a common coordinate system—Global Coordinate System
North American Datum of 1983 Canadian Spatial Reference System (GCS NAD83 CSRS) and
clipped to the CMH Galena operational area in ArcGIS. Raster data sets were aligned so that the
location and resolution of all raster were identical. An example subset of the data used in the
analysis is shown in Figure 8.
Methodology
The methodology employed in this study is based on the rationale that models of the
distribution of avalanche susceptibility can be generated using a fuzzy logic analysis of
morphological parameters and used to identify potential release areas. The output of this model
can be combined with a data set the linear geometries of GPS tracks of guided ski descents
through a spatial analysis to explore the exposure of heli-skiing guides to avalanche terrain.
Avalanche susceptibility and potential release are modeling
The avalanche susceptibility model developed in this study builds upon the multi-scale
fuzzy logic approach for the identification proposed potential release areas developed by
Veitinger et al. ( 2016). The model is based on four parameters: slope, wind shelter index, vector
terrain roughness, and forest stem density (Figure 10).
48
Figure 9: PRA Algorithm
The algorithm (Figure 9) employs a fuzzy logic intersection operation to combine the
parameters in order to derive a model of avalanche susceptibility represented by potential releas
area (PRA) class membership. A binary classification scheme of potential release areas is then
derived from the PRA class membership through the application of a threshold criterion. Cauchy
membership functions are used to model the membership of the various geomorphological
parameters. The algorithm requires four mandatory inputs to be provided: a DEM, a forest stem
density raster, a prevailing winter seasonal wind direction value, and a wind direction tolerance
value.
49
Figure 10: PRA algorithm parameters for the Magic Fingers ski run area
50
The algorithm extends and adapts the approach used by Veitinger et al. (2016) . A forest
density parameter was added to the model to improve the algorithm’s performance in forested
terrain. The parameterization of the Cauchy membership function for slope gradient was
modified to better represent the distribution of slope in human-triggered avalanche records.
Finally the calculation of Plattner et al.’s (2004) wind-shelter index was refined to be appropriate
to the of the DEM used in this study. The algorhithum does not employ the multi-scale
approach used by Veitinger et al.( 2014), to model the influence of snow depth distribution of
winter surface morphology, since re-scaling the 0.75 arc-second DEM data this study employs
would result in an undesirable loss of resolution. The algorithm is implemented in R (version
3.0.3) and makes use of the geo-computation and terrain analysis functions of the raster (Hijmans
et al., 2014) and RSAGA packages (Branning, 2008). The Markup for the algorithm is included
in Appendix A.
Slope gradient and aspect are calculated from the DEM by fitting a six parameter second
order polymodal to a 3x3 neighborhood (Evans, 1972) using the SAGA_GIS ta_morphologhy
module. Slope is returned in degrees from the horizonal and aspect is returned in degrees from
North, measured clockwise. The algorithm considers slopes between 25o and 55o degrees as
potential release areas. The degree membership in the PRA class
}’“”Š•
,
$
.
EGW
is modled by a
Cauchy membership function that approximates the distribution of slope angle in human
triggered avalanche accidents (Figure 1). The mean slope angle for human triggered avalanches
is 39o. Slopes with gradients of less than 30 and greater than 50 are assigned lower membership
values since human triggered avalanches become less likely (Figure 11).
The wind shelter index (Winstral et al., 2002) is calculated from the DEM using the
RSAGA wind.shelter function. A focal function fitted to a circular neighborhood of specified
radius is used to model the upwind influence of terrain on snow distribution. The direction from
51
which the prevailing wind originates, and the directional tolerance must be specified. The
returned topographic wind shelter index is a proxy for snow accumulation on the lee side of
topographic obstacles. For this study wind direction was specified to be 225 o with a 15o
tolerance based on historical records from weather telemetry within the study area.
Wind redistribution in mountainous terrain is generally restricted to an area of roughly
250m from a source feature (Raderschall et al., 2008). For the 0.75 arc second resolution DEM
employed in the study a neighborhood radius of 13 cells results in an analysis window that
approximates this range. A known limitation of the wind shelter index is that large wind
sheltering effects can be outweighed for high resolution DEMs, if the surrounding area is open to
wind influence. However, the CDEM data is not as susceptible to problem. As a result the wind
sheeter parameter is calculated using the maximum slope values in the rather than the third
quantile implemented by Veitinger et al (2016).
Wind shelter index varies between -1.5 and 1.5 in complex alpine terrain. Negative
values are retuned for terrain features that are exposed to the specified wind direction. The
degree membership in the PRA class
}–—ˆ/
,
$
.
EGW
is modeled by a Cauchy membership function
that assigns higher membership values to lee slopes and lower membership values to windward
terrain (Figure 11).
The vector dispersion method (Sappington et al., 2007) is used to calculated surface
roughness from the slope gradient and aspect. The degree membership in the PRA class
}˜”™~š
,
$
. is modeled by a Cauchy function that assigns high membership values for even and
smooth terrain features, with lower membership values in increasingly rough terrain. The
susceptibility to avalanches strongly decreases for roughness values between 0 and 0.001.
Between 0.01 and 0.02, avalanches are unlikely but possible. Above 0.02, avalanches are not
52
expected to occur (Figure 11). This correlates with roughness values found in previous studies
(Veitinger et al., 2013).
Forest density measured in total stems per hectare is parametrized using the spacing
between tree stems in forested terrain. Values are taken directly from the forest density raster.
The degree of membership in the PRA Class
}€”˜•’›
,
$
.
E
is modeled by a Cauchy membership
function that approximated the empirical relationship between forest density values avalanche
occurrences in forested terrain proposed by Viglietti et al. (2010) and supported by expert
interpretation. Higher membership values are assigned to open terrain and low density forested
areas where forest cover cannot hinder avalanche release. Lower membership values are
assigned to higher density forests that provide mechanical anchoring to the slope and disrupt the
formation of continuous week layers in the snowpack. Open terrain or forested glades with
spacing of 30m or more between stems (15stems/ha) have no preventative effect on avalanche
formation. Potential release areas become less likely in forests with 15m spacing between stems
(60stems/ha) and PRA membership values decrease with increasing forest density between 60
stems/ha and 350 stems per hectare. Below 450 stems/ha avalanches are unlikely to occur
(Figure 11).
The parameterization of the Cauchy membership functions is presented in Table 7. The
PRA membership functions for the 4 parameters are combined using the fuzzy AND operator.
a
b
c
Slope
7
2
38
Wind Shelter Index
2
3
2
Vector Roughness
0.01
5
-0.007
Forest Density
350
2
-120
Table 7: Cauchy membership function parmaterization
53
Figure 11: Cauchy membership functions for PRA class parameters
The confirmed avalanche release areas raster is used for model validation. True and false
positive rates are calculated over a range of 50 thresholds and plotted in a ROC curve using the
R package TOC (Pontius et al., 2015). The area under the ROC curve is calculated to evaluate
the performance of model independent of threshold selection. A binary classification scheme that
classifies all slopes between 25o and 55o as potential release area is used as a performance
54
benchmark. The performance of the model is also compared to the results of Veitinger et al.’s
(2016) PRA algorithm.
Avalanche susceptibility is modeled through the PRA class membership. A classification
threshold is then the used to convert the continuous PRA class membership into a binary PRA
classification scheme. The minimum distance and maximum Youden Index threshold are
calculated to suggest appropriate classifiers.
Spatial Analysis
The continuous avalanche susceptibility model and the potential release area
classification scheme are then used to explore the spatial relationships between guides’ terrain
usage and avalanche hazard.
A spatial intersection analysis between the linear geometry of the GPS-tracks and the
binary PRA classification scheme is used to test the hypothesis that guides reduce their exposure
to terrain capable of producing avalanches large enough to bury or kill a person when avalanche
hazard is higher. The binary PRA classification raster is first converted to a polygon layer and
polygons representing non-potential release areas (PRA value of 0). Vector geometry is then
calculated for each remaining feature and polygons with an area of less than 2500m2 are
removed as these are considered to be too small to produce an avalanche of sufficient size to
bury or kill a person.
The geometric intersection of the PRA polygon feature class with the GPS tracks
polyline feature class is calculated using the Intersect tool in arcGIS’s Overlay Toolset. Portions
of the GPS tracks polylines that intersect PRA polygon features are output to a new feature class.
The attribute table for this class is exported to R and histograms are generated to quantify the
exposure of guides to potential release areas at different hazard ratings.
55
In order to test the hypothesis that guides chose terrain that is less susceptible to
avalanches during periods of higher hazard PRA class membership values are extracted from
each raster cell that the GPS track polylines touch using “extract” function from the R package
raster (Hijmans et al., 2014). The daily PM hazard ratings, are then merged with the terrain
values of each of the extracted raster cells using the R package sarp (Haegeli et al., in prep).
Cells with a PRA class membership value of 0 are exclude from the analysis. The correlation
between the between hazard and the PRA class membership values of the terrain used is then
modeled though a categorical quantitative regression analysis using the R package quantreg
(Koenker, 2015).
Results
Potential Release Area model
The CMH Galena tenure is comprised of 3,380,389 raster grid cells. Figure 12 through
Figure 15 shows the distribution of the PRA class membership values for the different model
parameters across the study area.
Figure 12: Distribution of PRA membership for slope gradient across the study area
56
`
Figure 13: Distribution of PRA membership for wind shelter index across the study area
Figure 14: Distribution of PRA membership for vector roughness across the study area
57
Figure 15: Distribution of PRA membership for forest stem density across the study area
Figure 16: Distribution of PRA class membership
The PRA class membership was calculated as the fuzzy intersection of these parameters.
Figure 16 shows the distribution of PRA class membership across the study area. Since degree of
compensation,
œ
, is uniquely defined for each raster grid cell in the model it can be informative
to analyze the Person Correlation between each parameter and the model output (Table 8) (Wu
58
and Hung, 2016). Slope gradient and forest cover have the greatest correlation on PRA
membership whereas wind shelter and roughness have a less strong correlation.
•žŸ ¡¢
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£
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•¨ ©ª«
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0.452
0.248
0.213
0.408
Table 8: Pearson correlation ion coefficient between the parameter membership functions and the PRA class membership
Veitinger et al’s (2016) multi scale fuzzy logic PRA algorithm was implemented for the
study area using the same DEM, and wind direction/tolerance values. Given the large resolution
of the CDEM data used for the analysis, the algorithm’s terrain smoothing parameter for this
implementation was set to 1 to reduce information loss to rescaling. The predictive performance
of both models was measured against the confirmed avalanche release area raster through a ROC
curve analysis (Figure 17). AUROC values were calculated for both algorithms and used to
compare model performance. This analysis demonstrates that updated fuzzy logic model
provides an improvement in AUROC performance and achieves higher levels of model
sensitivity over Veitinger et al’s implementation.
Figure 17: ROC plot of the updated PRA class membership (left) and ROC Plot of Veitinger et al’s (2016) initial implementation
PRA class membership (right)
0.67
59
Both the minimum distance and Max Youden Index approaches to threshold section
recommended a threshold criterion of 0.06. This was used to generate a binary PRA classifier
from continuous PRA membership class. The performance of this classifier was assessed by
comparing its specificity and sensitivity to a Binary slope-based classification of potential release
areas (Figure 18). Previous studies have found this benchmark difficult to beat. The PRA
algorithm provides an improvement in classifier performance with a 4% improvement in model
sensitivity and a 3% improvement in model specificity (Table 9).
Figure 18: Fuzzy logic PRA classification with a membership threshold of 0.06 (left), binary slope-based classification (right)
Sensitivity
Specificity
Fuzzy logic PRA classification
0.74
0.30
Binary slope-based classification
0.71
0.32
Table 9: Performance comparison of binary PRA classifier and binary slope-based classifier
Exposure of GPS Tracks to Potential Release Areas
Overall the set of 6641 GPS tracks intersected PRA polygon features 16077 times. This
can be interpreted as: on average of guides encounter terrain features capable of producing
avalanches large enough to bury or kill a person 2.420 times per run. Figure 19 shows histograms
60
for the distribution of PRA intersection at the different elevation bands and at hazard levels.
Figure 19: GPS track intersecting PRAs at various hazard ratings in the Magic Fingers area.
Number of Intersections: GPS Tracks and PRAs
PM Hazard
Elevation Band
BTL
TL
ALP
Total
1
2681
2234
482
5397
2
2678
3298
745
6721
3
781
1396
296
2473
4
104
256
360
61
5
Not Assessed
379
545
202
1126
Total
6623
7729
1725
16077
Number of GPS Track Segments
PM Hazard
Elevation Band
BTL
TL
ALP
Total
1
2449
1749
469
4667
2
2415
2703
863
5981
3
716
1280
413
2409
4
122
258
2
382
5
Not Assessed
308
347
189
844
Total
6010
6337
1936
14283
PRA Intersections per GPS Track Segment
PM Hazard
Elevation Band
BTL
TL
ALP
Total
1
1.0947
1.2773
1.0277
1.1564
2
1.1089
1.2201
0.8633
1.1237
3
1.0908
1.0906
0.7167
1.0266
4
0.8525
0.9922
0.0000
0.9424
5
Total
1.1020
1.2197
0.8910
1.1256
Table 10: Summary of GPS track segments with PRA polygons
The results summarized in Table 10 illustrates validate the hypothesis that guides reduce
the frequency of their exposure to terrain capable of producing avalanches large enough to bury
or kill a person when avalanche by 19% between from a hazard rating of 4 and a hazard rating of
1. However, the degree to which they do so is not constant across elevation bands. The
reduction in exposure is most pronounced in alpine terrain and least pronounced in below
treeline terrain Figure 19.
62
Figure 20: distribution of hazard for GPS track intersections with PRAs
3,979,327 raster grid cells were extracted along the lines skied by guides. After filtering
for non-zero PRA class membership values, the analysis dataset included 1684603 observations.
The overall the median PRA class membership for all the slopes skied was 0.12914 (Table
11). Violin plots (Figure 21) show that the conditional distributions of PRA class membership
values under the different hazard ratings are heavily skewed. This is expected since the main
portion of helicopter ski runs is often accessed by traversing low angle slopes with low from the
63
helicopter landing and to the helicopter pickup, guides often also ski ‘warm-up’ and a ‘cool-
down’ runs that are in terrain less susceptible to avalanches regardless of the current hazard
rating (Haegeli and Atkins, 2010)
Hazard
Rating
PRA Class Membership
Min
1st Quantile
Median
Mean
3rd Quantile
Max
1
0.0001
0.06091
0.17232
0.25736
0.38437
0.91557
2
0.0001
0.03862
0.12078
0.19483
0.25934
0.91476
3
0.0011
0.03655
0.10166
0.15454
0.19641
0.91529
4
0.0042
0.02227
0.08493
0.11918
0.16327
0.87687
Total
0.0001
0.04420
0.12914
0.20599
0.27692
0.91557
Table 11: PRA class membership values extracted from GPS tracks by hazard rating
Figure 21: Violin plot of PRA class membership values extracted from GPS tracks by hazard rating
Due to the ordinal character of avalanche hazard ratings and the skewed distribution of
PRA’s an ordinal quantile liner regression was used to examine the relationship between the PRA
class membership values of terrain skied under each hazard rating over a range of quantiles
(Figure 22). The 90th quantile was selected, (
±"^•Z
) (Table 12) to represent the most severe
64
terrain skied at each hazard rating. This regression analysis demonstrates that guides chose
terrain that is less susceptible to avalanches as hazard increases. While mean and median PRA
index values show a slight decrease as hazard increase the trend becomes more pronounced for
more severe terrain.
Figure 22: Ordinal linear regression of PRA class membership and hazard rating over a range of quantile values
Rating
PRA (
±"^•Z
)
with respect to
hazard rating of
1
Std. Error
t-value
‚[
,
g
O
@
O.
Intercept
0.67734
0.00092
732.932
<0.00001
2
-0.15415
0.00132
-177.045
<0.00001
3
-0.29962
0.00174
-172.555
<0.00001
4
-0.39888
0.00228
-174.721
<0.00001
Table 12: Ordinal linear regression of the 90th quantile of PRA class membership and hazard rating.
65
Discussion
PRA model performance
This study demonstrates the opportunities and limitations for the application of fuzzy
logic potential release area models for regional scale analysis of avalanche susceptibility using
digital elevation and forest cover data readily available in Canada. The model presented
demonstrates an improvement in classifier performance over a binary slope-based classification
approach. The algorithm provides additional criteria for the partitioning of the geographic extent
of terrain capable of producing avalanches into sub-regions with higher avalanche susceptibility
by detecting terrain features that serve as borders for less extreme avalanches. Pearson
correlations was used to assess the influence of each of these parameters on the model outcome
Slope has the strongest correlation to PRA class membership and is the most important
parameter in the model influencing avalanche susceptibility. This corresponds to the role of slope
as a primary parameter in physical models of avalanche release. Slope angle serves as the best
indicator for the extent of terrain associated with extreme avalanche events where most or all of a
start zone area is released. Refining the slope parameter’s PRA membership function to better
approximate the distribution of slope across historical records of human avalanche accidents
increases the precision of the model in identifying slopes with the greatest potential for human
triggered avalanches.
Forest density was also found to have a strong correlation with PRA class membership.
This is appropriate given the influence that forest cover can have on inhibiting avalanche release
both by providing mechanical anchoring to the snowpack and interrupting the formation of
continuous weak layers. Previous avalanche susceptibility models have either used forested
terrain as a masking layer or treated open and forested terrain as equivalents. The addition of the
66
fuzzy forest density parameter allows for an avalanche susceptibility to be modeled as a function
of forest density improving the algorithm’s specificity in forested terrain. The inclusion of this
parameter is the main improvement of the algorithm over previous avalanche susceptibility
models.
The purpose of the vector roughness parameter is to model the continuity of terrain and
identify breaks in terrain that may separate neighboring release areas. Since the proportion of
such features is relatively low across the study region, it has only a weak correlation with the
PRA class membership over the entire study area. However, the inclusion of this parameter is
critical to breaking up the geographic extent of terrain susceptible avalanches identified by the
slope and forest density parameters into sub regions.
The wind shelter index parameter allows for avalanche susceptibility to be defined in
part by the prevalent wind direction. The purpose of the wind shelter parameter is to model the
large scale smoothing of terrain in lee features. As with the terrain roughness parameter, the
proportion of terrain where wind shelter may have an effect on avalanche susceptibility is
relatively low across the study area and the parameter has only a week correlation weak PRA
class membership.
The combination of refinements to the slope membership function and inclusion of a
forest density parameter resulted in a 7% improvement in performance measured by AUROC
when compared to the implementation of Veitinger et al.’s (2016) original algorithm for the same
study area. However, despite these improvements, there remain some significant limitations to
the model. Model performance can be evaluated against the larger context of geological hazard
models by a comparison of AUROC values from different studies. While the study’s AUROC
value of 0.72 is comparable to other natural hazard models validated against an in depended data
set it is lower than those of other continuous models of avalanche susceptibility that used higher
67
resolution digital elevation data (compare: (Yilmaz, 2016) - AUROC: 0.845; and (Veitinger et al.,
2016) - AUROC: 0.823).
Scale has a demonstrated impact on the derivation of the geomorphological parameters
employed in this study. The resolution of the DEM and extent of the measurement window must
be appropriate to the landscape feature being characterized. In the context of avalanche
susceptibility models, smaller spatial variations in avalanche susceptibility may go undetected if
the resolution is too course whereas terrain features that are buried by the winter snow pack may
be given undue consideration in the analysis if the resolution is too fine.
The vector roughness index calculated from the 0.75 arc second CDEM data is able to
detect coarse discontinuities in terrain such as major ridges and gullies that identify potential
borders between neighboring release areas. The use of course resolution DEMs in calculations of
terrain roughness has a smoothing effect of the terrain and so it does not require a re-scaling to
simulate the smoothing effects of winter snow cover. However, it is likely that there are
variations in slope shape or ground roughness present in winter terrain surface, which influence
avalanche susceptibility, and are not evident in the 0.75 arc second data. The measurement
extent of the wind index parameter accounts for the large scale smoothing of lee terrain features
as a result of snow redistribution by prevailing winds. However, as with the vector roughness
the DEM resolution is too large to capture the smaller slope-scale topographic-wind effects that
may influence the assessment of avalanche stability.
It is likely that variations in avalanche susceptibility exist at a smaller scale than the
model captures in the PRA class membership. The use of higher resolution data in the analysis
would likely result in improved model performance. However, high resolution DEMs are not yet
are widely available under free public use licenses and may be cost prohibitive for large study
areas. Furthermore, decreasing the grid size comes at an increased computational cost. As a
68
result, DEM resolution needs to be balanced against the spatial scale of the analysis and the use
of lower resolution DEMs may be the most appropriate for regional studies such as this.
The need to de-fuzzify the PRA membership class in order to generate a Binary PRA
classifier presents a further challenge. Defining an adequate threshold criterion requires a
subjective judgement about the costs of misclassifications in the context of the model’s
application. In this case a threshold was selected to identify terrain with potential to produce
avalanches large enough to bury or kill a person from the PRA class membership. The threshold
selected using the Youden Index in an attempt to maximizes the improvement in model
sensitivity over a random guess classifier. This threshold was also recommended by the
minimum distance approach that prioritizes model sensitivity and specificity equally. Although
the classification scheme produced by this threshold performed better as a predictor than a binary
slope-based classifier, it is likely that the model remains overly conservative.
Threshold selection was based on an incomplete dataset. The confirmed avalanche
release area polygons delineated by the guides do not represent all the terrain capable of
producing avalanche large enough to burry or kill a person in the study areas. As a result, false-
false positives are inherently more likely in the model than false-false negatives. Selecting a
threshold that prioritized sensitivity and specificity equally may have resulted in an overly
conservative threshold. However, it is impossible to determine how pronounced this effect may
be and assessing appropriateness of this prioritization remains an unsolved task in the model
design.
Relationship between hazard and exposure to potential release areas
The results of the analysis support the hypothesis that guides reduce the frequency of
their exposure to potential release areas and use terrain that is less susceptible to avalanches as
hazard increase. An important advancement in this studies approach is that it expert assessment
69
and uncertainty is factored into the analysis though the use of a fuzzy logic model of avalanche
susceptibility. Previous studies in this field have decoupled terrain parameters in order to
examine the interactions effects between terrain attribute. However, this approach requires that
their combined effects on the terrain usage patterns of guides to be modeled through either
weighed linear combinations which result in sharp and arbitrary transitions and breaks in the
modeled effect.
The analysis of the frequency of guides exposure to potential avalanche release areas is
the less informative of the two metrics explored in this study. However, it has value as a proxy
for the magnitude of the risk management tasks of heliskiing guides. Data on the frequency of
guides exposure to potential release areas could be coupled with heliskiing accident statistics to
develop meaningful measures on how successful guides are at choosing appropriate terrain for
the avalanche hazard.
The skewed distribution of the PRA class membership values over hazard rating can
partly be attributed to the fact many of the terrain choices guides make during a day may not be
due to avalanche considerations. Examining the quantile regressions of PRA class membership
over hazard for the 90th quantile shows a general relationship between the most severe terrain
skied and avalanche hazard. However, this ignores other operational influences that may affect
the terrain choices on a particular day or run. A way to exclude this effect would be to filter the
dataset to only include raster cells that were above the 90th percentile PRA membership class
values for each operational day prior to the regression analysis. This approach would eliminate
observations that are less informative in examining the relationship between terrain choices and
avalanche hazard.
Furthermore, the linear ordinal regression used in this analysis assumes that data points
are independent however this may not be the case for the extracted raster PRA membership class
70
values. Data points are taken from the same runs, on the same days and produced by the same
guides. Furthermore, guides are confined to a downhill direction of travel so the terrain choices
available to them are controlled by the terrain choices they have already made. While these
variables are not factored in to the regression of PRA class membership against hazard rating,
they do affect the data structure. One way to take this panel structure of the data into account
would be to have used a mixed effects linear regression model.
Even though the dataset of GPS tracks is substantial, the results of the study are limited
because the tracks only represent terrain choices from three winters and the terrain usage of
guides may change based on seasonal climatic trends (Thumlert and Haegeli, 2016) .
Furthermore, the CMH Galena exhibits a particular snow and avalanche climate. To ensure that
the terrain usage patterns are more representative, and the results of the analysis can be
generalized, future studies should include data from more winters and geographic regions.
Future research.
This study represents a first attempt at adapting modern avalanche susceptibility
algorithms for regional analysis using readily available DEM data. It also presents a new
approach to capture the terrain use of professional heliskiing guides with respect to avalanche
hazard. While the approach exhibits promise it can only be viewed as a proof of concept. The
resolution of DEM data freely available in Canada is a limitation that results in an overly
conservative model. Despite this limitations method, the analysis employed in this study can be
used to generate metrics that provide that objective and unbiased assessment of terrain usage
could be performed by an operation. If implemented in near real time this approach be used to
document and check for potential issues such as “exposure creep” or the tendency to increase
other potentially hazardous decision-making by one or more guides due to a range of external
influences. behaviours in a guiding team.
71
A more rigorous analysis of the correlation between PRA exposure and avalanche hazard
could lead to even more powerful operational tools. Conditional probabilities could be derived
for each hazard rating from an ordinal logistic regression of PRA values extracted along the ski
tracks. This could inform a model of terrain that guides deemed acceptable for skiing at a
particular hazard rating. Mapping such conditions specific terraing guidance could be a
poteintally powefull decision support tool.
Conclusion
In this study GIS was used in the spatial analysis of heli-skiing guides’ exposure to
avalanche terrain. A fuzzy logic model of avalanche susceptibility was introduced and used to
identify potential avalanche release areas in the CMH Galena’s heliskiing tenure in the Columbia
Mountains of British Columbia. This model was combined with the GPS tracks of more than
6,000 guided ski descents through two distinct spatial overlay analysis to explore the exposure of
heli-skiing guides to avalanche terrain.
The potential release area identification algorithm presented in this study analyzes the
avalanche susceptibility of terrain and detect discrete potential release areas over a regional scale
using data freely available in Canada. Four landscape parameters are included in the model
slope gradient, vector roughness, wind shelter index and forest density. Slope gradient, vector
roughness and wind shelter index were generated from 0.75 arc second resolution Canadian
Digital Elevation Model data. Forest density data was extracted from British Columbia’s
Vegetation Resource Inventory dataset. The algorithm was implemented in R.
The model’s fuzzy logic method is appropriate for mapping avalanche susceptibility,
especially in large or remote regions where avalanche location data may be limited or
unavailable. Cauchy membership functions were developed for each of the 4 landscape
parameters based on a review of the literature and expert assessments. The performance of the
72
model was assessed by using the AUROC technique. The avalanche susceptibility of terrain is
modeled by the continuous PRA class membership generated through the fuzzy intersection of
these 4 parameters. A classification threshold was selected from the analysis of the model’s ROC
curve to transform the continuous PRA class membership output into a binary classification
scheme for potential avalanche release areas. This classification scheme provided superior
model performance to a binary slope-based classification of potential release areas, commonly
used as a performance benchmark in similar studies.
An intersection analysis of GPS tracks with polygons representing potential avalanche
release areas supported the hypothesis that heliskiing guides reduce the frequency of their
exposure to potential release areas as hazard increases. An ordinal linear regression analysis of
the PRA class membership values extracted along the line geometry of the GPS tracks supported
the hypothesis that guides reduce their exposure to terrain susceptible to avalanche as hazard
increases.
The methodology presented demonstrates a proof of concept. Further data from be
gathered from different snow avalanche climates, and over more winters before these results are
generalized. The approach shows promise as a tool for monitoring operational risk and
transferring operational knowledge with a guiding team. An even more rigorous analysis of the
correlation between guides terrain with respect to avalanche susceptibility and avalanche hazard
could lead to the development of powerful evidence-base risk management decision making
models.
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APPENDIX
Fuzzy logic potential avalanche release area algorithm
Author: Andrew Eirik Ainer Sharp
Date: June 22, 2018
## Loading required package: knitr
# Enter input parameters
inputRas <- "DEM.asc" # input DEM
forestRas <- "forest.asc" # forest density raster
outRas <- "PRAindex.asc" # output raster
booleanRas <- "boolean.asc" # validation raster
maskRas <- "mask.asc" # validation mask
wind <- 225 # wind direction: N= 0, W =90, S=180
windTol <- 15 # wind tolerance
# Defines the Cauchy membership function
cauchy <- function(x, a, b, c) 1/ (1+((x-c)/a)^(2*b))
# Load R libraries
library(sp)
library(gstat)
library(methods)
library(plyr)
library(raster)
library(RSAGA)
library(RColorBrewer)
library(bit)
library(TOC)
# set environment
setEnv <- rsaga.env(workspace=work_dir,
path="C:/Program Files/SAGA-GIS",
modules="C:/Program Files/SAGA-GIS/modules")
# Import Data
asc <- raster(inputRas)
asc.extent <- extent(asc)
head <- read.ascii.grid.header(inputRas)
plot(asc,
col=terrain.colors(10),
main="Digital Elevation Model (m)\nCHM Galena",
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
writeRaster(asc, "sagaDEM", format="SAGA", overwrite=TRUE)
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#### Computation of slope gradient and aspect rasters using the RSAGA ta_morphometry
module ###
rsaga.geoprocessor("ta_morphometry",23,env=setEnv,list(
DEM ="sagaDEM.sgrd",
SLOPE="slope",
ASPECT="aspect_name",
SIZE=1,
TOL_SLOPE="1.00000",
TOL_CURVE="0.000100",
EXPONENT="0.00000",
ZSCALE="1.000000",
CONSTRAIN=FALSE))
rsaga.sgrd.to.esri("slope", "slope",
format = "ascii", georef = "corner", prec = 2)
# set slope and aspect values to NA outside of extent of DEM raster
slope <- raster("slope.asc")
slope[is.na(asc)] <- NA
writeRaster(slope, "slope", format="ascii", overwrite=TRUE)
rsaga.sgrd.to.esri("aspect", "aspect",
format = "ascii", georef = "corner", prec = 2)
aspect <- raster("slope.asc")
aspect[is.na(asc)] <- NA
writeRaster(aspect, "aspect", format="ascii", overwrite=TRUE)
rm(slope,aspect)
# Computation of windshelter index raster using a maximum search distance or radius
(dmax) of 300m to define the upwind window
# Input DEM is aggregated to a larger resolution DEM to improve computational
efficiency
windRaster<-aggregate(asc, fact= 2,expand=TRUE)
writeRaster(windRaster, "windRaster", format="ascii", datatype='FLT4S', overwrite=TRU
E)
ctrl <- wind.shelter.prep(8, (wind*pi)/180, (windTol*pi)/180 , res(asc)[1])
focal.function("windRaster.asc",fun=wind.shelter,prob = 1, control=ctrl, radius=8 ,se
arch.mode="circle")
## [1] "windshelter.asc"
rm(windRaster)
windShelter <- raster("windshelter.asc")
# Windshelter raster is resampled to the original DEM's resolution
windShelter <- resample(windShelter, asc, method= "bilinear")
plot(windShelter,
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col=heat.colors(10),
main="Wind Shelter\nCMH Galena Tenure",
sub= paste("Prevailing wind:", wind, "Tolerance:", windTol, sep=" "),
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
writeRaster(windShelter, "windShelter", format="ascii", overwrite=TRUE)
rm(windShelter)
### Computation of ruggendess raster
#create raster object of slope raster
slope <- raster("slope.asc")
aspect <- raster("aspect.asc")
#convert to radians
slope_rad <- slope*pi/180
aspect_rad <- aspect*pi/180
#calculate xyz components
xy_raster <- sin(slope_rad)
z_raster <- cos(slope_rad)
x_raster <- sin(aspect_rad) * xy_raster
y_raster <- cos(aspect_rad) * xy_raster
xsum_raster <- focal(x_raster, w=matrix(1,3,3), fun=sum)
ysum_raster <- focal(y_raster, w=matrix(1,3,3), fun=sum)
zsum_raster <- focal(z_raster, w=matrix(1,3,3), fun=sum)
ruggedness_raster <- (1-sqrt((xsum_raster)^2+(ysum_raster)^2+(zsum_raster)^2)/9)
writeRaster(ruggedness_raster, "ruggedness", format="ascii", overwrite=TRUE)
ruggedness_raster<-raster("ruggedness.asc")
plot(ruggedness_raster,
col=rev(heat.colors(10)),
main="Ruggedness\nCMH Galena Tenure",
sub="Sappington (2017) Vector Ruggedness Measure",
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
rm(slope, aspect, xy_raster, z_raster, x_raster, y_raster, xsum_raster, ysum_raster,
zsum_raster, ruggedness_raster)
# define bell curve parameters for slope
a <- 7
b <- 2
c <- 38
slope <- raster("slope.asc")
cauchyS <- function (x) cauchy(x, a, b, c)
85
curve(cauchyS,
main="PRA Membership Function for Slope Gradient",
xlab="x",
ylab=expression(paste(mu["slope"], "(x)")),
from = 0, to = 90, n=90)
# generate Cauchy membership values raster for slope
slopeC <- cauchyS(slope)
slopeC[slope < 25] <- 0
slopeC[slope > 55] <- 0
plot(slopeC,
col=rev(heat.colors(10)),
main=expression(paste(mu["slope"], "(x)")),
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
h <- hist(slopeC, breaks=10, plot = FALSE)
h$density = h$counts/sum(h$counts)*100
plot(h,
main = "Histogram of PRA Membership for Slope Gradient",
xlab = expression(paste(mu["slope"], "(x)")),
xlim = c(0,1),
ylab = "Percentage (%)",
col = rev(heat.colors(10)),
freq = FALSE)
rm(slope)
# define bell curve parameters for ruggedness
a <- 0.01
b <- 5
c <- -0.007
rugg <- raster("ruggedness.asc")
cauchyR <- function (x) cauchy(x, a, b, c)
curve(cauchyR,
main="PRA Membership Function for Vector Roughness Index",
xlab="x",
ylab=expression(paste(mu["rough"], "(x)")),
ylim = c(0,1),
from = 0, to = 0.02, n=50)
# generate Cauchy membership values raster for roughness
ruggC <- cauchyR(rugg)
ruggC[rugg > 0.01] <- 0
plot(ruggC,
col=rev(heat.colors(10)),
main=expression(paste(mu["rough"], "(x)")),
86
xlab="UTM Wwsting Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
h <- hist(ruggC, breaks=10, plot = FALSE)
h$density = h$counts/sum(h$counts)*100
plot(h,
main = "Histogram of PRA Membership for Vector Roughness Index",
xlab = expression(paste(mu["rough"], "(x)")),
xlim = c(0,1),
ylab = "Percentage (%)",
col = rev(heat.colors(10)),
freq = FALSE)
rm(rugg)
# define bell curve parametrs for wind shelter
a <- 2
b <- 3
c <- 2
windShelter <- raster("windShelter.asc")
cauchyW <- function (x) cauchy(x, a, b, c)
curve(cauchyW,
main="PRA Membership Function for Wind Shelter Index",
xlab="x",
ylab=expression(paste(mu["wind"], "(x)")),
from = -1.5, to = 1.5 , n=30)
# generate Cauchy membership values raster for wind shelter
windshelterC <- cauchyW(windShelter)
plot(windshelterC,
col=rev(heat.colors(10)),
main=expression(paste(mu["wind"], "(x)")),
sub=expression(paste("Wind direction: 225"^"o", ", Tolerance: 15"^"o")),
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
h <- hist(windshelterC, breaks=10, plot = FALSE)
h$density = h$counts/sum(h$counts)*100
plot(h,
main = "Histogram of PRA Membership for Wind Shelter Index",
xlab = expression(paste(mu["wind"], "(x)")),
xlim = c(0,1),
ylab = "Percentage (%)",
col = rev(heat.colors(10)),
freq = FALSE)
rm(windShelter)
# define bell curve parameters for forest cover
a <- 350
b <-2.5
c <- -150
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cauchyF <- function (x) cauchy(x, a, b, c)
curve(cauchyF,
main="PRA Membership Function for Forest Stem Density",
xlab="x",
ylab=expression(paste(mu["forest"], "(x)")),
from = 0, to = 800, n=80)
# generate Cauchy membership values raster for forest stem density
forest <- raster("forest.asc")
forest <- extend(forest, asc, NA)
forestC <- cauchyF(forest)
plot(forestC,
col=rev(heat.colors(10)),
main=expression(paste(mu["forest"], "(x)")),
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
h <- hist(forestC, breaks=10, plot = FALSE)
h$density = h$counts/sum(h$counts)*100
plot(h,
main = "Histogram of PRA Membership for Forest Stem Density",
xlab = expression(paste(mu["wind"], "(x)")),
xlim = c(0,1),
ylab = "Percentage (%)",
col = rev(heat.colors(10)),
freq = FALSE)
rm(forest)
#### Fuzzy logic intersection operator
minvar<- min(slopeC, ruggC, windshelterC, forestC)
PRA <- (1- minvar)*minvar + minvar*(slopeC + ruggC + windshelterC+forestC)/4
plot(PRA,
col=rev(heat.colors(10)),
main=expression(paste("f"["c"], "(x)")),
sub= "Paramaters: Slope, Wind Shelter Index, Vector Roughness, Forest Stem Densi
ty",
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
h <- hist(PRA, breaks=10, plot = FALSE)
h$density = h$counts/sum(h$counts)*100
plot(h,
main = "Histogram of PRA Class Membership",
xlab = expression(paste("f"["c"], "(x)")),
xlim = c(0,1),
ylab = "Percentage (%)",
col = rev(heat.colors(10)),
freq = FALSE)
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writeRaster(PRA, outRas, format="ascii", overwrite=TRUE)
# calculate Pearson corelation coefficients for each paramater
PRAcorr <- function(x) {as.numeric(cor(values(x), values(PRA), use = "na.or.complete
", method = "pearson"))}
corr = c(PRAcorr(slopeC), PRAcorr(windshelterC),PRAcorr(ruggC), PRAcorr(forestC))
#### ROC analysis using confirmed avalanche release areas raster
boolean <- raster(booleanRas, package="TOC")
mask <- raster(maskRas, package="TOC")
index <- raster(outRas, package="TOC")
#create and plot the ROC curve
threshold <- c(0:50)/50
rocd <- ROC(index, boolean, mask, thres=threshold)
plot(rocd,
main = "Reciever Cperating Characteristic",
sub = paste("AUROC:", round(rocd@AUC, digits=2) , sep = " "))
#### Calculates threshold criteria and binary PRA classification scheme
# calculate max Youden index threshold
j <- rocd@table[2] - rocd@table[3]
jthreshold <- as.numeric(rocd@table[which(j==max(j)),1])
# calculate min distance thresold
d <- sqrt((1-rocd@table[2])^2+(rocd@table[3])^2)
dthreshold <- as.numeric(rocd@table[which(d==min(d)),1])
# Generate binary PRA classification scheme raster
threshold <- jthreshold
sz <- reclassify(index, c(0,threshold,0,threshold,1,1))
arg <- list(at=seq(0,1), labels=c("Non PRA", "PRA"))
color = c("grey", "red")
plot(sz,
main=paste("PRA Classification\n Threshold: ", threshold),
sub=paste("TPR = ", round(rocd@table[which(j==max(j)),2], digits=2), ", FPR = ",
round(rocd@table[which(j==max(j)),3], digits =2)),
col=color,
axis.arg=arg,
xlab="UTM Westing Coordinate (m)",
ylab="UTM Northing Coordinate (m)")
writeRaster(sz,"sz.asc", format="ascii", overwrite=TRUE)
