NHESSNatural Hazards and Earth System ScienceNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus GmbHGöttingen, Germany10.5194/nhess-15-723-2015Amalgamation in landslide maps: effects and automatic detectionMarcO.omarc@gfz-potsdam.dehttps://orcid.org/0000-0002-1238-991XHoviusN.Helmholtz Centre Potsdam, German Research Center for Geosciences
(GFZ), Telegrafenberg, 14473 Potsdam, GermanyInstitute of Earth
and Environmental Sciences, University of Potsdam, Potsdam, GermanyO. Marc (omarc@gfz-potsdam.de)2April201515472373327November201416December20148March2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/15/723/2015/nhess-15-723-2015.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/15/723/2015/nhess-15-723-2015.pdf
Inventories of individually delineated landslides are a key to understanding
landslide physics and mitigating their impact. They permit assessment of
area–frequency distributions and landslide volumes, and testing of
statistical correlations between landslides and physical parameters such as
topographic gradient or seismic strong motion. Amalgamation, i.e. the mapping
of several adjacent landslides as a single polygon, can lead to potentially
severe distortion of the statistics of these inventories. This problem can be
especially severe in data sets produced by automated mapping. We present five
inventories of earthquake-induced landslides mapped with different materials
and techniques and affected by varying degrees of amalgamation. Errors on the
total landslide volume and power-law exponent of the area–frequency
distribution, resulting from amalgamation, may be up to 200 and 50 %,
respectively. We present an algorithm based on image and digital elevation model (DEM) analysis, for
automatic identification of amalgamated polygons. On a set of about 2000
polygons larger than 1000 m2, tracing landslides triggered by the 1994
Northridge earthquake, the algorithm performs well, with only 2.7–3.6 %
incorrectly amalgamated landslides missed and 3.9–4.8 % correct polygons
incorrectly identified as amalgams. This algorithm can be used broadly to check
landslide inventories and allow faster correction by automating the
identification of amalgamation.
Introduction
Regional landslide maps are a crucial component of many landslide related
studies : they are necessary to improve our
understanding of landslide rupture mechanics and test conceptual models, to
produce landslide risk and vulnerability maps, to understand how different
climatic and tectonic mechanisms can trigger landslides, and to estimate how
mass wasting contributes to sediment production and landscape evolution
.
Such maps used to be created by manual mapping from remote sensed imagery,
often accompanied by partial field checks e.g.. Due to the high
cost and time associated with manual mapping of thousands or tens of
thousands of landslides over large areas, automated mapping techniques are
increasingly used
e.g..
These techniques have specific associated errors, amongst which amalgamation,
that is the bundling of several adjacent landslides into a single map
polygon, is prominent. Amalgamation typically occurs when the spatial density
of landslides is high and the resolution of images from which they are mapped
relatively low, making it difficult to differentiate multiple landslides in a
perturbed area. Automatic mapping algorithms designed to detect change of
surface properties, irrespective of the shape of the changed area are
especially prone to this effect. If uncorrected, amalgamation can lead to
severely erroneous results and interpretations in many domains. For example,
studies using landslide maps to estimate the volume of debris produced,
whether to understand sediment transfer dynamics
, organic matter mobilization
, average erosion rates
or mountain building ,
rely on empirical laws giving landslide volume as a function of landslide
area . In this approach,
landslide depth is assumed to scale with area, giving rise to strongly
non-linear area–volume relations, which assign disproportionate importance to
landslides with the largest surface areas. Accurate landslide area mapping,
differentiating precisely between individual events is therefore of the
essence . This also applies to studies considering the
area–frequency distribution of landslides, whether to assess landslide hazard
and risk associated with extreme events , or
to understand the underlying physics of the distribution
.
Finally, any attempt to understand the physics of landslide triggering from
mapped landslide patterns could suffer from the effects of incorrectly mapped
landslide outlines and the artificial prominence of large disturbed areas
.
Here, we survey why and where amalgamation can occur, and determine the
minimum error it has introduced to estimates of total landslide volume and
the area–frequency distribution of several landslide inventories.
Subsequently, we propose an algorithm able to automatically detect
amalgamation when provided with a raster file of polygon shapes and a digital elevation model (DEM).
Performance of this algorithm is tested on a representative subset of the
inventory of landslides triggered by the Northridge earthquake. We finish
with a short discussion of the benefits and limitations of this approach and
possible alternatives.
Landslide mapping and amalgamation
Most landslide inventories are derived from analysis of optical or
multispectral imagery, exploiting the typical texture, colour and spectral
properties of freshly disturbed areas . Often,
landslides are conspicuous because they clear vegetation that has a very
different appearance or radiation intensity spectrum. When landslides are
mapped as polygons, whether by men or machine, the general assumption is that
the polygon represents a single landslide, most often combining a scar area,
a deposit area and sometimes a runout area. A mapped polygon is therefore
assumed to contain direct or indirect information on the location and size
and, implicitly, the volume of one landslide but also potentially about the
slope where the landslide initiated and terminated, the runout distance, the
drop of potential energy, or the triggering mechanism, such as the local peak
ground acceleration or pore pressure at the time of failure.
Some polygons from the data set,
representing landsliding caused by the 2008 Wenchuan earthquake. Polygons are
colour coded by size (red being the smaller polygons) and overlaid on a DEM
and a river network. The density of landsliding is correctly estimated but
dozens of small landslides have been connected along slope or even across
rivers or ridges. Light orange and green polygons have total area larger than
1 km2.
Amalgamation, the combination of several individual landslides in a single
polygon, can be due to the actual coalescence of landslides, or the apparent
contiguity of disturbed areas in images with low resolution or poor contrast
between affected and unaffected areas (Fig. ). Indeed, where
landsliding is very dense, several adjacent landslides may have joint runout
areas or overlapping deposits, or scars separated by a distance too short to
be resolved by the available imagery. At a given resolution, multispectral
images contain more information than optical images, which may help in
delineating individual landslides but this does not always preclude
amalgamation in landslide mapping. Even where image resolution would permit
accurate mapping of individual landslides, amalgamation can occur when the
primary goal of the mapper is not to map landslide extent precisely, but
rather to rapidly evaluate the area affected by slope failure. This seems
common for maps predating widespread use of landslide area–volume
relationships as well as for more recent inventories, underlining the current
lack of care in avoiding or at least flagging amalgamation. In automatic
mapping, algorithms that are not object oriented will usually classify single
pixels based on their various bulk properties
. If adjacent pixels are classified as
disturbed, then the algorithm will combine them in a single polygon,
regardless of how many separate landslides are contained within. When image
resolution is not very high, then automatic algorithms can bundle hundreds of
small landslides, located within a limited area with high propensity to
failure, into a single, apparently very large landslide polygon.
(a), (b), (c): landslide polygons on a
DEM topography showing examples of amalgamation in the ChiChi and Northridge
inventories. Geometric and topographic inconsistencies that signal
amalgamation are specified as follows: RC for ridge crossing, CC for channel
crossing, MH for multi-headed, MA for multi-armed and SI for slope
inconsistencies.
(d), (e): some polygons mapped by after the Wenchuan
earthquake overlaid on a 15 m resolution ASTER image (d) and on a 2.5 m resolution SPOT
5 image (e) of the same area. Note the presence of amalgamation but also the significant
mapping extent exaggeration when mapping on low resolution relative to the landslide density.
A striking example of amalgamation can be found in the Jou-Jou Mountain area
of Taiwan, where pervasive shallow landsliding occurred during the Mw 7.6
ChiChi earthquake in 1999 (Fig. )
. In available maps, these landslides have been
merged into a few complex shaped polygons, blanketing the steep, gullied
hills and covering 9.8 km2. However, a separate, local survey has found
more than one thousand individual, shallow failures, many of which adjoined
without making larger landslides . Together,
these landslides had a total area of 7.22 km2, implying a significant area
exaggeration by the automated mapping procedure. The implications of this
extreme amalgamation are far reaching. For example, using common landslide
area–volume relations ,
the total volume of the six largest, automatically mapped polygons in the
area would be estimated at about 0.19 km3, with the largest polygon
(4.13 km2) alone contributing about 0.11 km3. If the total area occupied by
these six polygons is arbitrarily repartitioned into 1000 landslides of
roughly equal size, set by the characteristic local ridge spacing and slope
lengths of 100–150 m, then a 17-fold reduction of the estimated landslide
volume would result. This estimate could be refined with access to the local
landslide data ,
which can be seen to have a non-uniform area–frequency distribution with hundreds of landslides
with areas of 100 m2 and one landslide of 0.1 km2.
In this example, amalgamation of landslides is easily recognizable due to the
complex shape of polygons straddling multiple topographic features, with
surface areas much larger than permitted by the characteristic length scale
of the topography. Formally, the merging of several landslides can result in
a range of geometric or topographic inconsistencies, such as multi-branched
polygons, or polygons with orientations inconsistent with local topographic
slope or transgressing ridgelines or channels (Fig. ).
We consider that these features are unlikely characteristics of individual landslides, even though failure on multiple
scarps, divergence in runout, runout crossing rivers and spreading on the opposing valley
side or occasional overtopping of dividing ridges are known to happen.
Some polygons may also appear topographically and geometrically consistent,
although they are, in fact, a combination of several adjacent landslides
close to or below the resolution of available images, the combined effect of
which is to alter the visual or spectral properties of a larger area. This
blurring can conjugate amalgamation and an exaggeration of the area affected
by landslides, but it cannot be identified without use of very
high-resolution images (Fig. ). It is, therefore, out of the
scope of our study and remains a challenge and a caveat for landslide
mapping.
Data
The recognition of geometric and topographic inconsistencies in landslide
inventories is a key to identification of amalgamation of individual
landslides and mitigation of its effects. To develop a method for detection
of amalgams in large landslide data sets, and to evaluate the effects of
amalgamation on scientifically interesting derivatives of these data sets, we
have focused on earthquake cases. Large earthquakes can trigger many
thousands of landslides in a limited area, reducing the possible effects of
geological heterogeneity on landslide populations and their statistics.
Moreover, by focusing on landslides with a shared trigger mechanism, we have
removed potential complications due to the convolution of trigger-specific effects
from our analysis. Finally, earthquake-induced landslide populations tend to
span a very large range of landslide sizes, allowing robust computation of
area–frequency statistics, one of the key attributes affected by
amalgamation.
We have used five published inventories of earthquake-induced landslides, mapped
over areas of 103–104 km2. Together, these inventories cover a range
of mapping approaches from manual mapping with extensive field checking, to
fast automated mapping with limited supervision and verification. The 1994
Mw 6.6 Northridge earthquake in California triggered more than 10 000
landslides, which were mapped manually from air photos, with field checks at
selected sites . The same approach was used to
map more than 6000 landslides triggered by a Mw 7.6 earthquake in 1976 in
Guatemala . The 1999, Mw 7.6 ChiChi earthquake in
west Taiwan also caused severe landsliding, with more than 9000 landslides
larger than 625 m2 (25 m × 25 m) mapped manually from SPOT satellite imagery
. Finally, for the 2008, Mw 7.9 Wenchuan
earthquake in China, many different maps of coseismic landslides exist
,
allowing comparison of independent and broadly equivalent data sets. We have
used two catalogues containing 50 000 polygons apiece. One was mapped with a
semi-automatic algorithm using 2.5 to 10 m resolution SPOT 5 and EO-1 satellite imagery .
The other was mapped by hand, mainly from 15 m resolution ASTER imagery and locally higher resolution
imagery . In all these inventories, the entire area perturbed by a
landslide, including scar, runout and deposit, is delineated by a single polygon.
In addition to these five inventories, we have used Aster GDEM-30m data to
evaluate the topographic context of mapped landslide polygons and as an input
of our algorithm for detection of amalgams. In the case of the Wenchuan
earthquake, we have also used 15 m resolution ASTER images and 2.5 m resolution
SPOT 5 images from the epicentral area, taken shortly after the earthquakes,
to verify the different landslide maps.
Quantifying the effects of amalgamation
The earthquake-induced landslide inventories summarized above are too large
for comprehensive manual verification. To assess the possible effects of
amalgamation in these data sets, we have focused on the largest polygons in
each inventory. These polygons dominate landslide volume estimates and can
strongly influence the best fits to area–frequency distributions. Thus, by
checking and correcting a limited number of large polygons, the quality of
derivatives of landslide inventories can be substantially improved. In
checking individual polygons, we considered as anomalous any polygon
displaying a geometrical or topographical inconsistency such as branching,
traversing of ridges or rivers or orientation inconsistent with the local
topographic slope. These polygons were compared with local topographic data
and, when appropriate split to make residual polygons more consistent with
the general topography. Nevertheless it is clear that without high-resolution
imagery, many landslide polygons were redefined in a relatively crude way.
We have used published area–volume relationships to estimate the volume of
landslides from the mapped disturbed areas . It
was assumed that landslides with area > 100 000 m2 involved bedrock, and
that smaller landslides were mixed bedrock and soil failures. Landslide maps
typically do not distinguish between scar and deposit, lumping the two into one
area measure. According to , scars and deposits
have area–volume relations with the same power-law exponent, implying
constant size ratios between scar and deposit areas of 1.1 and 1.9 for mixed
and bedrock landslides, respectively. Hence, we have estimated the scar area
by dividing the mapped landslide area by 2.1 and 2.9 for mixed and bedrock
landslides, respectively, assuming that runout was equal to the scar length.
Then we converted scar area A, into volume V, for bedrock and soil
landslides with V=aAb with a=0.146 and 0.234 and b=1.33 and 1.41 for mixed
and bedrock landslides, respectively. Computed landslide individual and total
volumes appear to be consistent with field estimates for cases where the
whole perturbed area is mapped.
Amalgamation effect on landslide area–frequency distributions.
(a) Comparison between the raw data from the coseismic landslide
maps for the 1976 Guatemala and 1994 Northridge earthquakes and the corrected
catalogue where every amalgam larger than 100 000 and 10 000 m2 was
split, respectively. (b) For the 2008 Sichuan earthquake, several
landslide maps were published. Of these, the data
set is severely affected by amalgamation whereas the
data set is relatively exempt from amalgams.
Comprehensive landslide inventories have a typical area–frequency
distribution with a roll-over and a power-law decay with an exponent, ρ,
commonly within a narrow range of values . The
roll-over can be caused by censoring of the small landslides due to the
mapping resolution , but can also be related to the physics
of landsliding and the transition from cohesion-controlled to
friction-controlled hillslope stability with increasing landslide area and
depth . The roll-over and
power-law decay have also been attributed to a combination of the size
distribution of continuous local topographic slopes and the distribution of
moisture or increasing cohesion with depth
. We have assessed the impact
of amalgamation by comparing the area–frequency distribution of the original
data sets with that of our partially corrected data sets. Because the frequency
decay with increasing landslide size is usually modelled as a power-law, a
specific functional form does not have to be prescribed if we only consider
the distribution at areas ten times larger than the roll-over. For these
large areas we have obtained ρ with a linear least-square regression of
the log-transformed data (Fig. ).
In many cases a larger number of smaller polygons were also visibly
amalgamated, but we did not correct them, due to the effort and uncertainties
involved. Thus, the estimates of errors on total landslide volume and the
power law exponent of the landslide area–frequency distribution due to
amalgamation, presented below, are likely minimum values. Next, we review the
individual landslide inventories and highlight the varying degrees to which
they are affected by amalgamation and its effects.
Landslides induced by the 1976 Guatemala and 1994 Northridge earthquakes were
mapped in detail, apparently to record where landslides had occurred, but not
necessarily to distinguish the boundaries of individual landslides. We have
inspected all 356 polygons with an area larger 10 000 m2 in the Northridge
inventory and all 90 polygons exceeding 100 000 m2 in the Guatemala
data set.
Together, these polygons represent 56 and 73 % of the
uncorrected volume of the landslide populations of the Northridge and
Guatemala earthquakes, respectively. 162 out of 356 and 51 out of 90 of these
polygons were found to be amalgams of several landslides. They were split
according to their shapes and relation to the local topography. This resulted
in a reduction of the total volume of landslides by 16 % in the Northridge
case and 35 % in the Guatemala case, and an increase of the area–frequency
scaling exponent, by 16 and 22 %, from 1.57 and 1.33 to 1.82 and 1.62,
respectively (Fig. ). Because polygons smaller than the
threshold represent only 44 and 27% of the total volume, respectively, and
because they must be less amalgamated and have much smaller individual
volumes, their correction would likely add only a minor contribution to the
total volume change.
The ChiChi earthquake caused widespread landsliding in the mountains of
central west Taiwan. An inventory of these landslides
contains 9272 polygons in an area 150 times
larger than the Jou-Jou Mountain, mentioned above, with a total estimated
volume of about 0.73 km3. We have inspected all 173 polygons larger
100 000 m2, representing 85 % of the total uncorrected volume of the
ChiChi inventory. We have found that 100 of them needed corrections ranging
from the splitting of minor branches to the artificial fragmentation of the
largest polygons in the Jou-Jou Mountain area, where precise correction was
impossible. Together, these corrections resulted in a volume reduction of
38 % to 0.45 km3, but an insignificant increase of the area–frequency
scaling exponent by 5 %.
The two inventories for the Wenchuan earthquake have similar total landslide
areas and similar total numbers of landslides, even though the mapping of
extended further to the north along the
seismogenic fault. We have compared the maps where they overlap, along 150 km
of the fault trace, where the majority of landslides occurred (e.g. Fig. ).
There is good overall agreement between the data sets, but the manual mapping of
has clearly delineated many more individual slides
(Fig. ). Many examples of amalgamation are evident in the
data set (Fig. ),
and although there are some mapping discrepancies between the two inventories, this
appears to be the main difference between them.
It has resulted in a total landslide volume reduction of 69 %, from 6.30 km3
for the automated-mapping inventory to 1.96 km3
for the original manually mapped inventory of
. However, this inventory also contains
amalgamation artefacts (Fig. ). We have visually checked all
152 landslides larger than 300 000 m2, representing 51 % of the total
volume of the manual inventory (including landslides mapped in areas not
surveyed by ). Of these 87 required editing, leading to a
final landslide volume estimate of 2.3 km3 instead of 2.45 km,
equivalent to a modest reduction of 6 %.
The landslide polygon area–frequency distributions of the Wenchuan
inventories also differ significantly (Fig. ). First, the
amalgamated catalogue of yields a discontinuous
distribution, which does not exhibit the roll-over commonly observed in
well-mapped data sets
. Instead the
smaller polygons also have a decreasing frequency with increasing size, and
they appear to be relatively infrequent compared to medium to large slides.
In contrast, the manually mapped inventory has a area–frequency distribution
with a roll-over at 1000 m2. The exponent on the best-fit power-law for
this data set, after our correction for amalgamation is also much higher than
for the inventory, ρ=1.5 and ρ=1.0,
respectively, confirming the relative abundance of large, mostly amalgamated
polygons in the latter (Figs. , ). Correction for
amalgamation effects results in a slight rise of the scaling exponent of the
manually mapped inventory to ρ=1.6.
From these analyses it is clear that amalgamation can significantly distort
both landslide population volume estimates and the frequency distribution of
mapped landslide areas. However, the frequency distribution itself does not
necessarily betray amalgamation, and exhaustive visual screening can be
prohibitively time consuming. In the following section, we propose an
automatic algorithm, which can be used to differentiate correctly mapped and
amalgamated polygons and allow faster and more comprehensive cleaning of
affected data sets.
Automatic detection of amalgamation
Because amalgamation leads to geometric anomalies and unusual positions of
putative landslides in the landscape it is possible to detect amalgams simply
by looking at their shape and at the underlying topography. Following the
criteria defined in Sect. 2 (Landslide mapping and amalgamation) we have
developed an algorithm able to guide a mapper or an end-user towards
suspicious polygons, and facilitate a correction or an assessment of the
catalogue quality (see Supplement). The algorithm requires a DEM, a raster
made from the polygon shapefile and a text file with polygon ID and
information. Below, we present the operation of the algorithm and assess its
accuracy.
First, the algorithm considers the geometry of a landslide polygon. The
branching of polygons is the most common and visible effect of amalgamation.
This affects the relation between perimeter, P, and area A, of the
polygons, biasing amalgams towards high P. These attributes are easily
extracted from a landslide inventory with any GIS. A polygon with given P
and A can be compared to an ellipse of equal P and A, and aspect ratio
K. Using approximation, ellipse perimeter can be
written as:
P=π32b(K+1)-Kb2,
where b is the smallest radius. Since A=πKb2, it can be shown that
the perimeter of any ellipse varies as
P=3(K+1)2K-1πA.
Rearranging Eq. (2), K can be found from P and A as the solution of a
second order equation:
K=1249PπA+12-2+49PπA+12-22-4.
Thus, any polygon can be described easily and objectively by the aspect ratio, K, of
its equivalent ellipse. For reference, a circle would yield K=1, a square K=2.3 and
rectangle twice as long as wide K=2.7. A polygon with high K is more likely to be
incorrect whereas a polygon with K<2 has a compact shape from which any mapping error
cannot easily be recognized. Therefore, to accelerate the algorithm any polygon below a
critical aspect ratio, Kc, is assumed to be correct (Fig. ).
Flowchart of the algorithm for automatic detection of amalgamation.
The algorithm is provided in the Supplement. Inputs are used to individually
analyse polygons based on geometric and topographic characteristics,
following a series of conditional tests that lead to a polygon score. A score
of zero means that the polygon is considered clean and any other scores refer
to some sort of amalgamation. K is the equivalent ellipse aspect ratio (see
Eq. 3), Lmax is the length of the longest branch of a polygon,
RBc is an arbitrary critical length ratio and Sc is a
critical slope angle.
A high K value may signal amalgamation or simply an elongated landslide, for example due to long runout.
Therefore, K is a useful input parameter but ultimately it is necessary to explicitly
consider the geometry of the polygon. This is achieved by reducing the mapped polygons to
their skeleton with a standard image analysis method, which iteratively thins a solid
polygon to a branched centre-line (Fig. ). From this skeleton, branch
points and individual branches are easily found. However, even polygons with a relatively
simple shape may have skeletons with some branching points and small branches pointing towards a polygon corner or irregular side.
To eliminate these spurious branches, we impose an arbitrary threshold size ratio of
branches relative to the longest branch, RBc. A polygon with a main branch and several
smaller branches, all of which are shorter than the main branch by a factor 1/RBc or more
is considered to be a correctly mapped, single landslide (Fig. ). All
other polygons receive a score equal to the number of branches, longer than the longest
branch divided by RBc, reflecting qualitatively the degree of amalgamation.
Part of the Northridge landslide polygon inventory overlaid on a
hillshaded DEM. The skeleton raster output is shown for all polygons larger
than 1000 m2 and with K>=2 (35 polygons). Polygons with K<2 are
filled in white and considered clean. White labels show erroneous polygons
detected by the algorithm, with positive numbers giving the number of
secondary branches detected, -2 meaning ridge or river crossing and -1
indicating a slope smaller than 12∘. Red labels show incorrectly diagnosed
or dubious results within this sample. Polygons with skeleton but no labels
have been correctly classified as unamalgamated.
In a second step, the algorithm tests the consistency of a polygon with apparently
correct geometry, with the local topography. This is done by extracting the DEM elevation
along the longest branch of the polygon, which is assumed to be an adequate representation
of the pathway of the landslide. First, the algorithm checks that the highest and lowest
elevations along the branch coincide with the top and toe of the mapped landslide. A
violation of this condition typically signals that the branch traverses a ridge or valley
floor, or that two landslides were merged into a crescent shaped polygon, smooth enough
not to be identified as a likely amalgam by the first part of the algorithm.
If the polygon passes this second test, then a last check is made to see if the maximum
variation of elevation along the main branch is above the minimum slope for landsliding,
Sc (Fig. ). Polygons failing this test are typically oriented perpendicular
to the main topographic slope over long distances, as a result of the lateral merging of
several small, parallel failures along a ridge or cliff.
Thus, our algorithm is formally based on three adjustable parameters Kc,
RBc, and Sc. Of these, only RBc may be substantially tuned,
depending on the smoothness of the input raster, which in turn depends on the
landslide mapping technique and the raster resolution.
Sc is a physical parameter which should normally be close to a 10∘ threshold for
landsliding e.g., thus requiring minimal
tuning, unless the local substrate has exceptional properties. To minimize the number
of false negatives (i.e. undetected amalgams), Kc should be set at a low value of
about 2, so that only polygons without any geometrical complexity are screened out.
Setting Kc at a higher value can be useful to assess the degree of amalgamation and
isolate only those polygons that are likely to be composites of many landslides.
To assess the accuracy of the algorithm we have applied it to an inventory of
landslides triggered by the 1994 Northridge earthquake in southern California
. Within the bounds of the Santa Susana
Mountains, we manually screened all 2083 mapped polygons larger than
1000 m2 for amalgamation. This is close to the roll-over in the landslide
area–frequency distribution of the inventory, so that the test set
encompasses most of the landslide volume.
The Santa Susana subset is representative of the diversity of size and shape that
can be found in the Northridge inventory in its entirety. Of all polygons in the
subset, the amalgamation state of 136 (6.52 %) could not be ascertained visually.
These polygons were removed from the test data set before further analysis. Of the
remaining 1950 polygons, 617 amalgams and 1187 single landslides were correctly
classified by our algorithm. The algorithm missed 70 amalgams (3.6 % of false
negatives, that is undetected amalgams) and incorrectly classified 76 single landslides
as amalgams (3.9 % of false positives, that is correct polygons classified as amalgams)
(Table ).
About two thirds of all polygons classified as amalgams were detected using
the branching criterium, in part because it is the most easily detectable
feature but also because it is the first step of the algorithm. One third of
amalgamation cases were only diagnosed by the second step of the algorithm,
which considers the topographic context of a polygon.
Taking results from these two steps together, the overall accuracy of the algorithm
was very good, with 1804 of 1950 (92.5 %) polygons in the test set classified
correctly (Table ). Thus, our algorithm provides a relatively rapid and
accurate way to assess the quality of a data set and a partial guide to manual correction.
It can reduce the workload associated with manual splitting of amalgamated polygons, by
foreshortening the amalgam identification phase, and enhancing the detection of smaller
amalgamated polygons that may have only subtle distortions. However, the algorithm only
yields a minimal number of branches and the automatic and accurate splitting of complex
polygons based on detected branching geometry remains a challenge.
The algorithm can assess the quality of every polygon of an inventory as long
as the raster resolution is high enough for a polygon to be made up by at
least a few tens of cells, so that a skeleton can be defined. Therefore, at a
raster pixel size of 2 m, 100 m2 polygons would have about 25 pixels and
could be analysed by our algorithm.
This is lower than the usual roll-over of landslide area–frequency distribution
e.g.. DEMs with a high spatial
resolution will also yield better results and the accuracy of the detection is helped
by the fact that the algorithm uses raw elevation data rather than a local derivative
such as slope, which is calculated over several adjacent cells.
Confusion matrix of the algorithm tested on the 1950 independently
verified polygons larger than 1000 m2, from an inventory of landslides
triggered by the 1994 Northridge earthquake. Positive and negative conditions
refers to polygons considered amalgamated and correct, respectively.
Therefore, false positives are correctly mapped polygons erroneously
identified as amalgams whereas false negatives are amalgams that remain
undetected by the algorithm. Values are given as number of landslides and
percent of the total population. The algorithm was run with the following
parameters: resolution 2 m, Kc=2, Sc=12∘ and
RBc=5 for the upper part of the table and RBc=6
for the lower part.
We have proposed an algorithm based on polygon geometry and topographic
analysis, which allows automatic detection of polygons outlining amalgamated
landslides with good but incomplete detection rates and minimal diagnostic
error. However, depending on the objective of a study, even a few incorrectly
diagnosed polygons may be of concern.
Therefore, the algorithm must be tuned towards a reduction of false negative results,
by increasing RBc or Sc, even if the rate of false positive results increases as a
consequence. For example, raising RBc from 5 to 6 in the analysis of landslides in the
Santa Susana Mountains results in a useful 24 % reduction of false negative results,
from 70 to 52 polygons out of 1950, and a concomitant increase of false positive results
by 16 % from 76 to 90 polygons (Table ). However, increasing Sc to 15∘ or
more may increase significantly the number of false positives but not necessarily the number
of true positives as the most common type of amalgamation is related to multiple branches.
An increase of false positives is not an issue, if amalgams detected by the algorithm are
subsequently split manually.
In that case, the operator can decide to leave an incorrectly diagnosed polygon intact.
However, false negatives will go unnoticed and could have a large impact. Therefore, it is
advisable to perform an additional manual check of the largest polygons in a data set,
irrespective of how the classification algorithm has diagnosed them, especially for
applications where the importance of polygons is proportional to their size. For example,
one false negative within the 10 or 20 largest landslides in an inventory could significantly
affect estimated total landslide volume.
A second, more fundamental issue is that the algorithm considers polygon
geometry, in a way which does not allow detection of ellipsoid-shaped
amalgams. Examples of this can be found, amongst others, in an inventory of
landslides triggered by the 2008 Wenchuan earthquake
, where several landslides on the same slope
were sometimes merged into larger, relatively smooth, polygons with a low K
value and without any clear geometric or topographic indication of
amalgamation (Fig. ).
In this case, image resolution may have been too low to distinguish the separate
landslides, or the mapper may have simplified the geometry for convenience. For
such amalgams, even if another criteria, such as alignment of the polygon long axis
with the strike of the topographic slope, hints at possible amalgamation, high-resolution
imagery would be required to test the diagnosis, as single landslides with similar shape
and orientation may exist.
Merger of parallel landslide outlines due to image resolution limitations may
cause errors of similar magnitude as other types of amalgamation, which are
more easily detected, and could critically affect the common argument that at
a given pixel resolution small landslides are missed but everything above a
cutoff length scale of a few cells is properly mapped.
Because the high-resolution imagery required to check visually for the occurrence of
low-K amalgamation, or any other type of amalgamation, is rarely available to end-users
of landslide inventories, it is important that it is mitigated for by those who
develop the mapping techniques and acquire the landslide inventories. This may not
always concur with the principal objectives of a particular mapping effort, for
example in natural disasters when rapid assessment of the location and total extent
of landslides is of the essence. However, if a landslide inventory is to be of
general use to the research community, then the risk of amalgamation must be
suppressed, both in manual and automatic mapping.
Suppression of landslide polygon amalgamation is hampered by deeper issues,
such as image resolution and the uncontrolled subjectivity introduced in
binary landslide mapping, where every pixel either is or is not a landslide.
We draw into question the general assumption that in a given inventory, every
landslide larger than a few image pixels is correctly mapped
e.g.. Instead, it is reasonable to expect
that many disturbed areas mapped as single medium to large landslides could
in fact consist of groups of smaller landslides, giving potentially
significantly different erosion volumes and size statistics (Fig. ).
Moreover, satellite imagery does not always yield unambiguous
information about the number and shape of landslides, which occurred on a
given slope. Where this applies, subjective choices of the mapper are
crystallized within the landslide inventory.
A Bayesian approach to mapping, aimed at delivering probabilistic instead of binary
maps e.g. could be helpful in testing the different
possibilities of splitting complex disturbed areas (see Fig. ) and
ultimately deliver more accurate, objective and reproducible data sets.
Short of a practicable, comprehensive solution, our method, which has a good
reliability, can be used in several ways to mitigate for amalgamation in
landslide maps, by helping the mapper to identify mistakes in automatic
mapping, and the user to do the same in existing landslide maps. Notably,
sorting mapped polygons by K value and size allows rapid, first order
vetting of the largest landslides, which, when followed by manual splitting
of amalgams, will be enough to yield a reasonable estimate of the total
volume of landslides in an inventory.
Then, for large populations, one could exclude all polygons with K values above a
threshold and consider the correlation between the size or location of remaining
landslides and physical parameters such as local topographic slope or triggering
effects. Finally, a K value criteria might also be introduced in a semi automatic
algorithm detecting landslides, to guide iteratively towards a sound splitting of adjoining landslides.
In the end, we must recall that amalgamation even if it may be a major source
of errors, such as in the Wenchuan example, it is not the only one. Firstly,
anthropogenic clearance or other disturbance of the landscape may be erroneous
for a landslide, especially by automatic algorithms. Secondly, when scar,
transport and deposit areas cannot be differentiated the volume of landslides
with long runout may be substantially over-estimated. Thirdly, when
landslides are reactivated and previously stable parts of the landscape are
not implied, then it may be hard for the mapper to delineate the area of the
actual failure with accuracy and this new failure may also not yield a volume
as large as expected from area–volume relationships. These issues may
be difficult to deal with but their effects will be suppressed when high
resolution imagery is used by an experienced mapper. Additionally, systematic
ways of dealing with these issues, such as the flagging of reactivated
landslides, and the differentiation of the transport areas of debris flow or
long runout landslides should be practised by mappers and also considered by
users analysing old data.
Conclusions
We have shown that amalgamation, the bundling of several adjacent landslides
into a single map polygon is a common problem in landslide inventories that
has inflated estimates of landslide volumes by up to a factor of three, and
the power-law exponent of landslide area–frequency distributions by up to
50 %. Even though the design of a comprehensive and fully reliable automatic
corrective method remains a challenge, we have presented and tested a
practical algorithm for automatic detection of amalgamated polygons based on
geometric and topographic considerations.
The algorithm performs well with an accuracy of 92.5 % and only 2.7–3.6 % amalgams
missed and 3.9–4.8 % correct mapped polygons incorrectly classified. It can, therefore,
be used to automate the identification of landslide amalgams, accelerate the
evaluation of data sets, and guide the manual correction of amalgams.
Thus, our algorithm is a first step towards setting a quality standard for landslide
maps in order to derive scientifically and societally useful variables, such as risk
estimates, erosion rates, organic matter fluxes, or correlations between landsliding and
physical triggers, as accurately as possible. Further challenges lie in attempting to
automatically correct amalgamation and in assessing how mapping errors due to resolution
blurring propagate into final products derived from landslide maps.
The Supplement related to this article is available online at doi:10.5194/nhess-15-723-2015-supplement.
Acknowledgements
O. Marc is funded by a fellowship in the EU Marie Curie International Training
Network TOPOMOD, project reference number 264517.
The authors have gratefully used Aster GDEM V2, a product of METI and NASA.
The authors benefited from discussions with Jens Turowski and Patrick Meunier
on an earlier version of the manuscript and are grateful to Tolga Gorum and
Robert Parker for providing access to their landslide maps.
The authors thank C. T. Lee and an anonymous referee for their review that helped to improve the manuscript.
O. Marc and N. Hovius conceived the study and wrote the manuscript. O. Marc performed all
analyses and developed the algorithm, assisted by N. Hovius. The authors have no
conflicts of interest related to the work reported in this
paper.The article processing charges for this open-access
publication have been covered by a Research Centre of the Helmholtz Association.
Edited by: F. Guzzetti
Reviewed by: C.-T. Lee and one anonymous referee
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