Probabilistic Prediction Models for
Landslide Hazard Mapping
Chang-Jo F. Chung and Andrea G. Fabbri
Abstract
A joint conditional probability model is proposed to represent
a measure of a future landslide hazard, and five estimation
procedures for the model are presented. The distribution of
past landslides was divided into two groups with respect to a
fixed time. A training set consisting of the earlier landslides
and the geographical information system-based multi-layer
spatial data in the study area was used to construct the pre-
diction maps. The predictions were then cross-validated by
comparing them with the remaining later landslides. When the
database falls short of providing sufficient support for the
prediction, the model allows the introduction of the expert's
knowledge to modify the observed frequencies of the land-
slides with respect to the spatial data. The additional in-
formation should improve the prediction results. A case study
from the Rio Chincina region in Colombia was used to illustrate
the methodologies.
Introduction
Using spatial data sets based on geographical information sys-
tems (GIS) quantitative prediction models have been proposed
for landslide hazard mapping (Wang and Unwin, 1992; Carrara
et al., 1992; Chung and Fabbri, 1993; van Westen, 1993; Jibson
et al., 1998). We propose a unified probabilistic framework for
predictive modeling using GIS-based multi-layer spatial data.
In the probability models for the prediction of landslide hazard,
the hazard at each point or pixel is considered as the joint con-
ditional probability that the pixel will be affected by a future
landslide given (conditional to) the information from the spa-
tial input data at the pixel. We present five estimation proce-
dures for the models and also offer a new strategy for visualiz-
ing, interpreting, and validating the results of predictions.
The five procedures are (1) direct estimation of the joint
conditional probability for every pixel based on the past land-
slides; (2) estimation of the bivariate conditional probabilities
for the thematic classes in each layer using the past landslides
and then, based on them, computation of the joint conditional
probability at each pixel by the Bayesian formula under the
conditional independence assumption; (3) estimation as in (2)
of the bivariate conditional probabilities for the thematic
classes in each layer but under the assumption that the joint
conditional probability for every pixel is a linear function of
the bivariate conditional probabilities (the linear function is
estimated using regression analysis); (4) estimation identical to
(2) except that the estimated bivariate conditional probabilities
using the past landslides are modified using expert's knowledge
before being used to compute the joint conditional probability;
and (5) the combination of (3) and (4), again assuming that the
joint conditional probability for every pixel is a linear function
of the modified bivariate conditional probabilities (here, too,
the linear function is estimated using regression analysis).
Bayesian formulas for geologic prediction models were
used by Spigelhalter (1986) and Agterberg et al. (1990). Chung
and Fabbri (1993) have adapted the formulas for geologic haz-
ard zonation as a part of "favorability function" approaches,
and the method has been applied to landslide prediction by
Chung and Leclerc (1994, Leclerc (1994, Luzi (1995), and
Luzi and Fabbri (1995). Multivariate regression analysis for
landslide hazard was proposed by Carrara (1983), Carrara et al.
(1992), and more recently by Chung et al. (1995).
Although some layers of spatial data represent continuous
measurements, such as slope angles and distances, as dis-
cussed by Chung et al. (1995), a map layer containing continu-
ous measurements is usually converted into a number of
classes, i.e., "thematic classification," for producing a new map
representing geologic hazard. In general, we may assume that
each layer represents a classification map containing a number
of thematic classes. A case study from a region in central
Colombia, which is affected by rapid debris avalanches, is used
to compare these five procedures.
Study Area and Test Data Set in the Rio Chincina Area in
Central Colombla
The catchment of the Rio Chincina, located on the western
slope of the central Andean mountain range (Cordillera Cen-
tral) in Colombia, near the Nevado del Ruiz volcano, was used
as a test for various landslide hazard zonation techniques. Van
Westen (1993) made an extensive study of the region and con-
structed the database of the study area. Since then it was made
available as an "ideal" case-study data set for many kinds of
exercises and experiments on landslide hazard zoning by van
Westen et al. (1993), with the name of GISSIZ: training package
of Geographic Information Systems on Slope Instability Zona-
tion. It is with that data set that Chung et al. (1995) applied a
variety of methods of multivariate regression and reviewed
some of those settings as the basis of the analysis. This study
broadens the approach to a comparison of other methods in
which data-driven approaches and knowledge-driven ap-
proaches are considered in isolation and in combination to
identify the most successful strategies for hazard prediction.
The input data for landslide hazard zonation consist of sev-
eral layers of map information. Each layer may be the result of
map updating by experts, of field verification, and of interpreta-
tion of aerial photographs. The prepared maps for the analysis
C-J E Chung is with the Geological Survey of Canada, 601
Booth Street, Ottawa, Ontario KIA OE8, Canada.
(chung@gsc.nrcan.gc.ca).
A. G. Fabbri is with the International Institute of Aerospace
Survey and Earth Sciences (ITC), Hengelosestraat 99, P.O. Box
6, 7500 Enschede, The Netherlands, (e-mail: fabbri63itc.d).
Photogrammetric Engineering & Remote Sensing
Vol. 65, No. 12, December 1999, pp. 1389-1399.
0099-1112/99/6512-1389$3.00/0
O 1999 American Society for Photogrammetry
and Remote Sensing
PHOTOGRAMMETRIC ENGINEERING 81 REMOTE SENSING December 1999 1389

usually describe surficial and bedrock geology, including shear- TABLE 1. FREQUENCY RATIOS OF PRE-1960 OCCURRENCES OF RAPID DEBRIS
strength measurements for geologic units (Jibson et al., 19981, AVALANCHES IN EACH CWS AS AN ESTIMATOR OF THE BINARY CONDITIONAL
soil type, slope, land use, geomorphology, mass movements, PROBABILITY FUNCTION (COLUMN 2) AND A MODIFICATION (COLUMN 3) OF THE
distance from active faults, and other features which are rele- CONDITIONAL PROBABILITY FUNCTION BY EXPERT'S KNOWLEDGE FOR EACH CLASS USED I N THE ANALYSIS (COLUMN 1).
vant to slope instability. The preparation and the selection of
input layers for the analysis are obviously a crucial and impor- Pre-1960 Expert's
tant component of building prediction models for landslide Lithological Units Data Knowledge
hazard, but these are not the subject of this paper. In addition, unmapped area 0.020 0.010
the identification of types and dates of landslide phenomena is alluvial sediments 0.015 0.020
critical to the application of predictive techniques. gneissic intrusives 0.004 0.004
For the Rio Chincina study area, van Westen (1993 and per- flow materials, alluvial, ashes 0.010 0.010
sonal communications) has suggested that the seven data lay- lake deposits 0.017 0.020
ers-(I) bedrock lithological map, ( 2 ) geomorphologic map, (3) weathered debris flow 0.018 0.020
slope map, (4) land-use map, (5) three maps containing distance gabbro and diorite 0.001 0.001
from the nearest valley head, (6) road, and (7) fault-are "causal mix Of ~ ~ r r ~ ~ ~ ~ ~ ~ ~ ~ , debris *Ow 0.015 0.015
factors" and are significantly related to landslide hazards metasedimentary 0.020 0.020
andesitic intrusives 0.000 0.000
among the many layers described in van Westen (1993). The schists 0.001 0.000
corresponding classes in each layer are shown in the first col- tertiary sediments 0.016 0.016
urnn of Table 1. volcanic 0.017 0.017
In the spatial database, it was assumed that the time of the lahar deposits 0.051 0.050
study was the year 1960 and that all the spatial data available pyroclastic flow deposits 0.002 0.002
in 1960 were compiled, including the distribution of the scarps Pre-1960 Expert's
of the landslides shown in blue in Plate 1, which had occurred Geomorphological Units Data Knowledge prior to that year. The occurrences play a pivotal role in con-
structing prediction models by establishing probabilistic rela- unmapped area 0.020 0.010
tionships be-tween the pre-1960 landslides and the remainder Western hills 0.011 0.010
of the input data set. The predictions based on those relation- zone 0.015 0.020
ships were then evaluated by comparing the estimated hazard 0.010 0.005
classes with the distribution of the scarps of the landslides that Pre-1960 Expert's
had occurred after 1960, i.e., during the period 1961 to 1988 Land-Use Units Data Knowledge
shown in red in Plate 1. We have also used these seven layers baditional farming 0.005 0.006 to develop other predictive models for landslide hazard in technified farming 0.017 0.012
Chung et al. (1995) and Fabbri and Chung (1996). modern intermediate farming 0.000 0.000
other crops 0.014 0.010
Probability Model construction 0.012 0.010
Let A denote the whole study area. Suppose that we have m lay- bare 0.011 0.010
ers of spatial map data containing "causal" factors which are fizzt 0.008 0.008 known to correlate with the occurrences of future landslides in 0.006 0.008
A. Consider a pixel p in A with m pixel values, v,(p) = c, . a * , Slope Pre-1960 Expert's
v,(p) = c,, one for each layer. The prediction problem can be (degree) Data Knowledge
represented by the following task: aggregate the m pixel values 0-10 0.005 0.000
at pixel p in A as a function describing the support for the con- 10-20 0.010 0.010
dition thatp is likely to be affected by a future landslide. 20-30 0.020 0.020
To construct a probability model for landslide hazard, con- 30-40 0.025 0.030
sider the following proposition: 40-50 0.023 0.040
50-60 0.089 0.050
60-70 0.005 0.030 Fp: "p will be affected by a future landslide of 70-80 0.002 0.020
a given type D." (1) 80-90 0.000 0.010
Valley Head Pre-1960 Expert's
We propose that the hazard at each pixel p be expressed as the Distance Data Knowledge
following joint conditional probability:
>50m 0.011 0.010
25-50m 0.023 0.025
P d ~ ( F ~ l v ~ ( p ) , vz(p), vm(p)l (2) 0-25m 0.036 0.050
Road Pre-1960 Expert's
that p will be affected by future landslides given the m pixel Distance Data Knowledge
values, (v,(p) = c,, ..., v,,,(p) = c,).
At pixel p, the pixel value vl(p) of the first layer is c, which >50m 0.013 0.010 25-50m 0.012 0.015 is one of the n, classes (map units), (1,2, ..., n,]. Consider a set 0-25m 0.012 0.020
of all pixels whose value in the first layer is cl. The set is the
thematic class in the first layer whose pixel value is cl. The set Fault Pre-1960 Expert's
is denoted by A,,, and it is one of the non-overlapping n, sub- Distance Data Knowledge
areas {A,,, A,,, .--, A,,,} in the first layer. Similarly, we have >loom 0.012 0.010
A,,, for the second layer. Finally, we have m thematic classes 75-loom 0.017 0.014
A,,,, . . a , A, one for each layer, which correspond to the m 50-75m 0.013 0.016
input pixelvalues, vl(p) (=cl), .-., v,(p) (=c,) at p. The pixel 25-50m 0.014 0.018
p is one of the common pixels contained in all m thematic 0-25m 0.014 0.020
classes A,,,, . a - , A,,,.
1390 December1999 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING