Modeling debris slide travel distance
1
Bogdan Strimbu1,2, John Innes1
Forest Resources Management Department
University of British Columbia
Vancouver, British Columbia, Canada
2
Email: strimbu@interchange.ubc.ca
Abstract
A travel distances model for debris slides is presented based on information collected in southeastern
British Columbia, Canada. The model was developed with two objectives: to produce the minimum
confidence interval for prediction and to consider the uncertainty associated with recorded data. The
model incorporates a variable that represents terrain morphology by a single number, which increases the
predictive efficiency of the model as event travel distance is mostly driven by terrain variation. Multiple
regression analysis was used to model the dependence of event travel distance on terrain morphology,
slope, stand height, terrain curvature and canopy closure (R2=0.975, p<0.001). Same variables used in the
regression analysis were then fuzzified to capture data values vagueness. Fuzzy regression method was
used to predict debris slide travel distance. The research found that for events less than 200 m fuzzy
regression supplies more accurate predictions while crisp regression performs better on longer events.
Introduction
Landslides are the geomorphic process with a significant impact on the human society, mainly the result
of their frequency and occurrences. To reduce the influence of these catastrophic events on the human
built infrastructure an accurate description of the mechanisms characterizing the terrain failure initiation
and travel distance is necessary. This study elaborated a new methodology to calculate the runout
distances for debris slides occurring in forested areas.
Methodology
A set of 39 events collected in southeastern British Columbia, Canada and described as debris slides
(Cruden & Varnes 1996), were used in model elaboration (Figure 1).
Figure 1. Study area
The model was developed with two objectives: to produce the minimum confidence interval for prediction
and to consider the uncertainty associated with recorded data. The size of the confidence interval depends
on the performances of the regression used to model the landslide travel distance (Mosteller & Tukey
1977). The magnitude of the debris slide travel distance is driven by terrain morphology (Wu & Sidle
1995). Therefore, the model incorporates a variable that represents terrain morphology by a single
number, which is obtained using one-to-one correspondence between binary and decimal numeration
systems (Strimbu 2002).
Multiple regression analysis was used to model the dependence of event travel distance on different
attributes characterising terrain geomorphology, soil and vegetation. The regression equation
performances depend not only on the amount of variables used in analysis but also on the number of
assumptions violated or not during analysis. Consequently, as a part of the modeling process, the equation
selected to predict the landslide travel distance has to fulfilled all the assumptions and requirements
imposed by regression analysis (Neter et al. 1996).
Same variables used in the crisp regression analysis were then fuzzified to capture data values vagueness
(e.g. soil depth and glanulometry, canopy closure and terrain curvature). (Tanaka et al. 1982) fuzzy
regression method was used to predict debris slide travel distance.
The performances of both regression equations, crisp and fuzzy, were assessed on an independent data set.
The testing data set was determined using the methodology proposed by (Snee 1977).
Results and Discussions
The method proposed to code terrain morphology has a site-specific character, providing a flexible
representation of local conditions. This increases the predictive efficiency of the model as event travel
distance is mostly driven by terrain variation rather than other environmental attributes.
Several hundred of equations were tried to fit the data set. The final crisp regression equation contains as
predictor variables terrain morphology, slope, stand height, terrain curvature and canopy closure
(R2=0.975, p<0.001).
L=f[ (log( path + 1))1.2 , (cos α)5, (
h +1 5
) * (1 + sin ϕ ) , convexity × 1/(k+0.01)]
10
path - the variable quantifing slopem morphology
α - event azimuth
ϕ - event slope
h - average stand hight
convexity - terrain convexity
k - canopy closure of event first reach
The model fulfills all of the assumptions and requirements of regression analysis (i.e. normality,
homoscedasticity, non-correlated errors, multi-colinearity, outliers). Fuzzy regression equation used,
besides the significant variables identified in crisp analysis, the slope and stand height independently:
L=f[ (log( path + 1))1.2 , (cos α)5, (
h +1 5
h +1 5
) * (1 + sin ϕ ) , (
) , sin ϕ ,convexity × 1/(k+0.01)]
10
10
Fuzzy model predicted all test events, and two outliers, while crisp regression predicted all of the test
events but only one outlier (α=0.05). For short events (less than 200 m) fuzzy regression supplies more
accurate predictions while crisp regression performs better on longer events (Figure 2).
Figure 2. Comparison of the crisp set and fuzzy sets models
Conclusions
Fuzzy set offers a realistic approach to the scientific investigation. The usual weakness associated with
vagueness of the attributes is not every time valid (Klir & Yuan 1995). The non-linear programming
approach, proposed by (Tanaka et al. 1982)proved to overcome the wide confidence intervals which are
the result of fuzzy set arithmetic. The proposed method, a combination of fuzzy set and crisp sets, proved
to supply the best results for debris slide travel distance.
Both equations (crisp and fuzzy) are easy to implement in any GIS software and can be used in risk
assessment associated with different forest activities (e.g. harvesting or road building)
References
Cruden,D.M. and Varnes,D.J. 1996. Landslide Types and Processes. In Special Report 247: Landslides
Investigation and Mitigation. 2 ed. National Academy Press, Washington D.C. pp. 36-71.
Klir,G. and Yuan,B. 1995. Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall, Upper
Saddle River.
Mosteller,F. and Tukey,J.W. 1977. Data Analysis and Regression: A Second Course in Statistics.
Addison-Wesley, Boston.
Neter,J., Kutner,M.H., Nachtsheim,C.J., and Wasserman,W. 1996. Applied linear statistical models. 4 ed.
WCB McGraw-Hill, Boston.
Snee,R.D. 1977. Validation of Regression-Models - Methods and Examples. Technometrics 19: 415-428.
Strimbu,B.M. 2002. Prediction of unconfined debris slide-flow travel distance using set theory. University
of British Columbia, Vancouver.
Tanaka,H., Uejima,S., and Asai,K. 1982. Linear regression analysis with fuzzy model. IEEE Transactions
on Systems, Man and Cybernetics 12: 903-907.
Wu,W.M. and Sidle,R.C. 1995. A Distributed Slope Stability Model for Steep Forested Basins. Water
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