Today avalanche research primarily focuses on the reliable prediction of avalanche descents
by using meteorological data and snowpack properties. This thesis complements these
approaches by providing means to automatically categorize snow proles into ten predened
templates, which may be used as an indicator whether potential avalanches might carry o
deeper layers of snow to form avalanches of higher magnitude. For this purpose, the snow
hardness prole is taken and transformed into a symbolic internal data format based on
weighted strings. This representation allows for the application of well-known methods
such as string alignments, which provide the foundation for the classication system.
Furthermore, as a secondary strategy, the class-templates themselves are modied in a neat
way that does not distort their overall shape, thereby providing matching candidates for a
larger portion of input proles. Altogether, the proposed system converts the input prole
into the internal representation, takes each of the modied template versions and determines
a proper alignment of hardness layers as the basis for a nal error score computation that
enables an ordering among the contemplable template types. The work in this thesis may
be generalized to approach a wider range of problems and is closely related to the eld of
time series data mining.
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Categorization of Snow Profile Data into Predefined Class Templates
1. Leopold-Franzens-University Innsbruck
Institute of Computer Science
Categorization of Snow
Profile Data into
Predefined Class
Templates
MASTER THESIS
Christian Schaiter
Academic advisors: Univ.-Prof. Dr. G端nther Specht
DI Robert Binna
2. Content
What you may expect in the next 15 minutes...
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
2
3. Overview
Current chapter: Introduction
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
2
4. Introduction and motivation
Aim of the thesis
Master thesis was done in cooperation with the Tyrolean
avalanche warning service (TAWS)
Goal: Find a way to
determine the potential
magnitude of an
avalanche
Categorization of Snow Profile Data into Predefined Class Templates
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5. Introduction and motivation
Snow profiles, hardness profiles, template types
TAWS frequently takes snow profiles from different areas
Most relevant property of a snow profile for this thesis:
Hardness profile
Hardness
profile
Snow height [cm]
Snow hardness
Categorization of Snow Profile Data into Predefined Class Templates
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6. Introduction and motivation
Snow profiles, hardness profiles, template types
Some example hardness profiles (collected from the TAWS):
Categorization of Snow Profile Data into Predefined Class Templates
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7. Introduction and motivation
Snow profiles, hardness profiles, template types
Idea: Introduce a group of predefined hardness profile types
(template types, class templates)
These template types describe the overall composition of the
snowpack
They may be used to
Profile types (class templates)
estimate the magnitude
of avalanches
10 types defined so far
Categorization of Snow Profile Data into Predefined Class Templates
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8. Introduction and motivation
Snow profiles, hardness profiles, template types
Goal: Automatically find the associated profile type for
each collected hardness profile
Reject hardness profile if no reasonable profile type is found
Profile types (class templates)
Snow height [cm]
Hardness profile
Determine type
Snow hardness
Categorization of Snow Profile Data into Predefined Class Templates
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9. Overview
Current chapter: Overview of the developed system
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
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10. Overview of the developed system
Schematic view of the proposed classification system
Categorization of Snow Profile Data into Predefined Class Templates
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11. Overview
Current chapter: Alignment of hardness profiles
1
Introduction and motivation
2
Overview of the developed system
3
Alignment of hardness profiles
4
Conclusion
Categorization of Snow Profile Data into Predefined Class Templates
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12. Alignment of hardness profiles
Representation format of hardness profiles
Hardness profiles may be viewed as
time series (clockwise rotated by 90属)
Height corresponds to time axis
Hardness values map to the amplitude
dimension
Desired properties of an internal data
format:
Height independence
Shape preservation
90属
Local height warping
Categorization of Snow Profile Data into Predefined Class Templates
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13. Alignment of hardness profiles
Representation format of hardness profiles
Hardness profiles may be viewed as
time series (clockwise rotated by 90属)
Height corresponds to time axis
Hardness values map to the amplitude
dimension
Desired properties of an internal data
format:
Height independence
Shape preservation
Local height warping
Categorization of Snow Profile Data into Predefined Class Templates
matching
11
14. Alignment of hardness profiles
Hardness profiles as weighted strings
Idea: Use symbolic representation (weighted strings)
A weighted string is composed of weighted characters
Direction character:
D (down), U (up)
Height (as a percentage)
6
5
4
3
2
1
Hardness difference
(among adjacent layers)
Compact form uses only
direction characters
D
D, 0.15, 1.5
U, 0.05, 3.5
D
U
D, 0.35, 0.5
D
D, 0.1, 1
D, 0.05, 3
U, 0.1, 6
D, 0.05, 1.5
D, 0.15, 1
D
D
U
Categorization of Snow Profile Data into Predefined Class Templates
D
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15. Alignment of hardness profiles
Principle of hardness profile alignment
Hardness profiles are aligned based on their compact strings
Weights are required to calculate a penalty score
Goal: Find a global alignment with a maximum number of
matching characters (optimal alignment)
Edit transcript describes operations (match M, deletion D,
insertion I) required to transform the first string into the second
String alignment examples
The compact string UUDUD and DUDUU may be aligned as
U U D U D
D U D U U
I D M M I M D
or
U U D U D
D U D U U , etc
D D M M M I I
Categorization of Snow Profile Data into Predefined Class Templates
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16. Alignment of hardness profiles
Principle of hardness profile alignment
Well-matching profile
U D D U U D D D
U D D D U D D D
M M M I D M M M M
Categorization of Snow Profile Data into Predefined Class Templates
Badly-matching profile
U D D U U D D D
U D
M D M D D D D D
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17. Alignment of hardness profiles
Calculation of optimal alignments
Algorithms for calculating optimal string alignments:
Categorization of Snow Profile Data into Predefined Class Templates
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18. Alignment of hardness profiles
Calculation of optimal alignments
Categorization of Snow Profile Data into Predefined Class Templates
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19. Alignment of hardness profiles
Computation of penalty scores
After all optimal alignments have been found: Compute penalty
scores
2 types of penalties:
Match-penalty
for differences in:
- Height
- Hardness
Mismatch-penalty
for mismatching blocks
- Much more severe
Categorization of Snow Profile Data into Predefined Class Templates
match-penalty
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21. Conclusion
What you have heard in the last 15 minutes
Template types are used to
estimate magnitude of avalanches
Classification is based on string
alignment techniques
Well matching strings
similar
hardness profiles
Achieved success rate of > 90% for
example set (if not rejected)
Approach may be used for any time
series data
Categorization of Snow Profile Data into Predefined Class Templates
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23. Backup slides
Distance measures: Cosine of angle, Euclidean Distance
Similarity measure: Cosine of angle
Dissimilarity measure: Euclidean Distance
Euclidean Distance:
Take the smallest distance
between points
in the vector space
Categorization of Snow Profile Data into Predefined Class Templates
Cosine of angle:
Take the smallest angle
between vectors
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24. Backup slides
Problems with the Euclidean Distance
Consider the hardness profile
(in blue) and its dedicated
template (in green)
In principle they are
well-matching
Nevertheless, a large error
occurs (in red) when applying
the Euclidean Distance
measure
ED does not handle height
warps
Categorization of Snow Profile Data into Predefined Class Templates
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25. Backup slides
Calculation of optimal alignments
Compute a distance table (with dynamic programming)
Example: Compact strings UUDUD and DUDUU
Categorization of Snow Profile Data into Predefined Class Templates
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26. Backup slides
Calculation of optimal alignments
Based on the distance table, compute the edit graph and
perform a traceback
U U D U D
D U D U U
D D M M M I I
U U D U D
D U D U U
I D M M I M D
Categorization of Snow Profile Data into Predefined Class Templates
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27. Backup slides
Template type duplication
Template type versioning:
Create different versions with multiple gradation steps
Categorization of Snow Profile Data into Predefined Class Templates
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28. Backup slides
Template type duplication
Variations of template type versions:
Scale up one layer at the cost of the other layers
Categorization of Snow Profile Data into Predefined Class Templates
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29. Backup slides
Profile matching
Alignment of hardness layers: Limitations
Example should be of type 4, but perfectly matches type 3
Categorization of Snow Profile Data into Predefined Class Templates
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30. Backup slides
Profile matching
Alignment of hardness layers: Limitations
Problem of deceptive local extremes
Causing false negatives
badly matching
perfect match
Categorization of Snow Profile Data into Predefined Class Templates
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31. Backup slides
Profile matching
Alignment of hardness layers: Limitations
Problem of abusing misalignments
Causing false positives
Apparently wrong profiles may achieve too good penalty scores
(see examples)
Categorization of Snow Profile Data into Predefined Class Templates
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32. Backup slides
Genetic Algorithm principles
Mechanics of a simple Genetic Algorithm: 5 Steps
Step I: Encoding of the search domain with a small alphabet
Step II: Creation of an initial string population
Step III: Reproduction of strings
Step IV: Crossover of strings
Step V: Mutation of strings
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