GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-9-3975-2016Automatic delineation of geomorphological slope units with r.slopeunits v1.0
and their optimization for landslide susceptibility modelingAlvioliMassimilianomassimiliano.alvioli@irpi.cnr.itMarchesiniIvanhttps://orcid.org/0000-0002-8342-3134ReichenbachPaolaRossiMaurohttps://orcid.org/0000-0002-0252-4321ArdizzoneFrancescahttps://orcid.org/0000-0002-1709-2082FiorucciFedericaGuzzettiFaustoCNR IRPI, via Madonna Alta 126, 06128 Perugia, ItalyMassimiliano Alvioli (massimiliano.alvioli@irpi.cnr.it)9November20169113975399113May201621June201617October201619October2016This 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://gmd.copernicus.org/articles/9/3975/2016/gmd-9-3975-2016.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/9/3975/2016/gmd-9-3975-2016.pdf
Automatic subdivision of landscapes into terrain units remains a challenge.
Slope units are terrain units bounded by drainage and divide lines, but their
use in hydrological and geomorphological studies is limited because of the
lack of reliable software for their automatic delineation. We present the
r.slopeunits software for the automatic delineation of slope units,
given a digital elevation model and a few input parameters. We further
propose an approach for the selection of optimal parameters controlling the
terrain subdivision for landslide susceptibility modeling. We tested the
software and the optimization approach in central Italy, where terrain,
landslide, and geo-environmental information was available. The software was
capable of capturing the variability of the landscape and partitioning the
study area into slope units suited for landslide susceptibility modeling and
zonation. We expect r.slopeunits to be used in different
physiographical settings for the production of reliable and reproducible
landslide susceptibility zonations.
Introduction
The automatic subdivision of large and complex geographical areas, or even
entire landscapes, into reproducible, geomorphologically coherent terrain
units remains a conceptual problem and an operational challenge.
Terrain units (TUs) are subdivisions of the terrain that maximize the
within-unit (internal) homogeneity and the between-unit (external)
heterogeneity across distinct physical or geographical boundaries
.
A slope unit (SU) is a type of morphological TU bounded by drainage and divide
lines ,
and corresponds to what a geomorphologist or an hydrologist would recognize as a single slope,
a combination of adjacent slopes, or a small catchment.
This makes SUs easily recognizable in the field, and in topographic base maps.
Compared to other terrain subdivisions, including grid cells or unique-condition units
, SUs are related to the hydrological and geomorphological
conditions and processes that shape natural landscapes. For this reason, SUs are well
suited for hydrological and geomorphological studies,
and for landslide susceptibility (LS) modeling and zonation
.
SUs can be drawn manually from topographic maps of adequate scale and quality
. However, the manual delineation of SUs is time-consuming
and error-prone, limiting the applicability to very small areas. Manual
delineation of SUs is also intrinsically subjective. This reduces the
reproducibility – and hence the usefulness – of the terrain subdivision.
Alternatively, SUs can be delineated automatically using specialized software.
The latter exploits digital representations of the terrain, typically in the
form of a digital elevation model (DEM) , or adopts image
segmentation approaches .
In both cases, the result is a geomorphological subdivision of the terrain
into mapping units bounded by drainage and divide lines, which can be
represented by polygons (in vector format) or groups of grid cells (in raster
format).
Large and complex geographical areas or landscapes can be partitioned by
different SU subdivisions. Unique (i.e., universal) subdivisions do not
exist, and optimal (best) terrain subdivisions depend on multiple
factors, including the size and complexity of the study area, the quality and
resolution of the available terrain elevation data, and – most importantly
– the purpose of the terrain subdivision (e.g., geomorphological or
hydrological modeling, landslide detection from remote-sensing images,
landslide susceptibility, hazard or risk modeling). An open problem is that
an optimal SU subdivision for LS modeling cannot be decided unequivocally, a
priori, or in an objective way, and the quality and usefulness of a LS
zonation depends on the SU subdivision .
In this work, we propose an innovative modeling framework to determine an
optimal terrain subdivision based on SUs best suited for LS
modeling. For the purpose, we also present the r.slopeunits
software for the automatic delineation of SUs, and we propose a method to
optimize the terrain subdivision in SUs performed by the software. The
r.slopeunits software is written in Python for the GRASS GIS
, and automates the delineation of SUs, given a DEM and a set of
user-defined input parameters. We tested the r.slopeunits software
and the proposed optimization procedure for LS modeling in a large area in
central Italy, where sufficient landslide and thematic information was
available to us .
The paper is organized as follows. First, we present the proposed approach
for the delineation of an optimal terrain subdivision into SUs best
suited for LS modeling, based on an optimization method
(Sect. ). Next (Sect. ), we present the
method for the automatic delineation of SUs, which we have implemented in the
r.slopeunits software for the GRASS GIS, and (in Sect. )
we describe a segmentation metric useful for the evaluation of the SU
internal homogeneity. Next, we introduce landslide susceptibility modeling
(Sect. ) and our optimization approach to the SU partitioning
(Sect. ). This is followed (in Sect. ) by a
description of the study area, in central Italy, and of the data used for LS
modeling. In Sect. , we present the results obtained in our
study area in central Italy; then we summarize the obtained results
(Sect. ), and outline possible uses of the
r.slopeunits software and of the optimization procedure
(Sect. ).
Modeling framework
We propose a new modeling framework for the parametric delineation of
SUs and their optimization, as a function of a few input
parameters, for the specific purpose of determining landslide susceptibility
(LS) adopting statistically based classification methods
. The
framework is exemplified in Fig. , and consists of the following
steps:
First, the r.slopeunits SU delineation software – described in Sect. ,
and whose flowchart is shown in Fig. – is run multiple times with
different combinations of the input modeling parameters.
Each software run results in a different subdivision of the landscape into a different set of SUs.
In each run, the number and size of the SUs depend on the input modeling parameters.
Second, the internal homogeneity and external inhomogeneity of each SU subdivision
– required by any meaningful terrain subdivision – are defined in terms of terrain aspect,
measured by the circular variance of the unit vectors perpendicular to the local topography
represented by all grid cells in a slope unit.
For each set of SUs obtained in step 1 using different input parameters,
the quality of the aspect segmentation is evaluated adopting a general-purpose segmentation
objective function, presented in Sect. .
At the same time, for each set of SUs obtained in step 1, a LS model is calibrated
adopting a logistic regression model (LRM) for SU classification (Sect. 5).
In the LRM, each SU is classified as stable (i.e., free of landslides) or unstable
(i.e., having landslides) depending on a (in our case, linear) combination of the local terrain
conditions (i.e., the geo-environmental variables).
The performance of the model calibration is evaluated using the
area under the curve (AUC) of receiver operating characteristic (ROC),
referred to as the AUCROC metric,
a standard and objective metric commonly adopted in the literature to evaluate the performance
of LS models .
Lastly, an overall (combined) objective function is defined by properly combining
the segmentation (step 2a)
and the AUCROC (step 2b) objective functions, as described in Sect. .
Maximization of this quantity allows to single out the optimal set of SUs (i.e., the optimal terrain subdivision)
that, simultaneously, (i) provides a good aspect segmentation and
(ii) results in an effective calibration of the LS model.
Maximization of the combined objective function allows selecting objectively the optimal
combination of the input terrain modeling parameters best suited for LS modeling (step 4 in Fig. )
and the corresponding SU subdivision.
Logical framework for the proposed method for (1) the parametric
delineation of SUs, (2a) the assessment of the quality of terrain aspect
segmentation using of a proper segmentation objective function, (2b) the
calculation and assessment of the quality of the LS modeling using a standard
AUCROC metric, and (3) the definition and maximization of a
combined objective function for (4) the determination of optimal parameters
for the delineations of SUs best suited for LS modeling and zonation.
In summary, the proposed modelling framework relies on an optimization
procedure that maximizes a proper, specific function that contains
information on (i) the morphology of the study area, represented by the
aspect segmentation metric (step 2a), and on (ii) the specific landslide
processes under investigation (in our case, slow- to very slow-moving shallow
slides, deep-seated slides, and earth flows), represented by the LS model
performance and the associated AUCROC metric (step 2b). The
optimization approach removes subjectivity from the SU delineation algorithm,
and produces a result that is objective and completely reproducible. This is
a significant advantage over manual methods , or
specialized software that needs multiple parameters and specific calibration
procedures.
Automatic delineation of slope units
Automatic delineation of SUs can be performed adopting two strategies. The
first strategy defines a large number of small homogeneous areas, and
enlarges or aggregates them progressively, maximizing the aspect homogeneity
of the SUs . Following this approach, the size of the initial
polygons representing the small homogeneous areas is significantly smaller
than the size of the desired (final) SUs, which results from the aggregation
of multiple areas performed maximizing an objective function
. The second strategy defines an initial small number of
large or very large areas, and progressively reduces their size until a
satisfactory result is obtained .
In the second strategy, the study area is subdivided into large
subcatchments, which can be further subdivided into left and right sides
(looking downstream with respect to the main drainage), with the resulting
two sides named half basins (HBs). The size of the initial HB is much
larger than the desired size for the SUs.
For both strategies, the final subdivision of the landscape into SUs does not
maintain memory of the terrain partitioning represented by the initial areas
or HBs. In both strategies, deciding when to stop the aggregation or the
partitioning to obtain a terrain subdivision suitable for a specific use (in
our case, LS modeling) is critical. Both strategies are subject to the
selection of user-defined modeling parameters, which introduce subjectivity
and reduce the reproducibility of the results. These are conceptual and
operational problems that hamper the design and the implementation of an
automatic procedure for the effective delineation of terrain subdivisions
based on SUs .
Slope unit delineation algorithm
For the delineation of the SUs, we adopt the second strategy outlined above,
i.e., we start from a relatively small number of large HBs, and we gradually
reduce their size by subdividing the HBs into smaller TUs. Hydrological
conditions and terrain aspect requirements control the subdivision of the
large HBs into smaller TUs. The approach is adaptive, and it results in a
geomorphological subdivision of the terrain based on SUs of different shapes
and sizes that capture the real (natural) subdivisions of the landscape.
We implemented the approach to the delineation of SUs in a specific algorithm,
coded in the r.slopeunits software (Fig. ). The
algorithm (and the software) uses the hydrological module
r.watershed available in the GRASS GIS. Using a DEM
to represent terrain morphology, r.watershed produces a map of HBs
adopting an advanced flow accumulation (FA) area analysis. Each grid cell in
the DEM is attributed the total contributing area FA, based on the number of
cells that drain into it. The FA values are low along the divides and
increase downstream along the drainage lines. This information is used to
single out streams and divides, i.e., the main elements bounding a SU
. The r.watershed module can use single
flow direction (SFD) or multiple flow direction (MFD) strategies. In the SFD strategy, water is routed to the single
neighboring cell with the lowest elevation, and in the MFD strategy water is
distributed to all the cells lower in elevation, proportionally to the
terrain slope in each direction. The r.slopeunits software adopts
the MFD strategy to distribute water to the neighboring cells.
Flowchart for the r.slopeunits software.
(a) Input data and parameters.
AP, (input parameter name: plainsmap) map showing plain areas
to be excluded from the processing;
DEM, (demmap) digital elevation model;
t, (thresh) initial FA threshold area;
a, (areamin) minimum area;
c, (cvmin) circular variance;
r, (rf) reduction factor;
maxarea, maximum SU area;
cleansize, size of candidate SU to be removed; see text for detailed
explanation.
(b)r.watershed processing in GRASS GIS .
(c) Tests if the produced HBs are in a plain area. (d) The
average area of each new HBchild in each HBparent is
checked against a. (e) HBchild is individually checked
against a and c requirements. (f) The process proceeds to
iteration i+1 for each and every HBchild that still does not
meet the requirements, with an updated ti+1=ti-ti/r FA threshold.
(g) Small polygons are removed from the candidate SU set.
The r.slopeunits software requires a DEM, demmap, accepts
an optional layer showing alluvial plains (APs), plainsmap, and the
following user-defined numerical parameters (Fig. a): (i) the
flow accumulation area (FA) threshold, thresh; (ii) the minimum
surface area for the SU, areamin (in square meters); (iii) the
minimum circular variance of terrain aspect within a
slope unit, cvmin; (iv) a reduction factor, rf; (v) the
maximum surface area for the SU, maxarea (in square meters,
optional); and (vi) a threshold value for the cleaning procedures,
cleansize (in square meters, optional; see
Sect. ). For simplicity, in the following we refer to the
numerical values of thresh, areamin, cvmin, and
rf as t, a, c, and r, respectively.
The software adopts an iterative approach to partition a landscape into SUs.
In the first iteration, r.watershed uses the threshold t
for controlling the partitioning into HBs. The parameter t has to be smaller
than the maximum surface accumulation area (FA) for the study area to allow
for the delineation of at least two HBs that are large enough to be further subdivided.
Grid cells with FA >t are recognized as drainage lines (i.e.,
streams), and used to delineate the river network by r.watershed,
grouping all grid cells in the DEM that drain into a given stream segment.
These cells collectively represent the catchment drained by the stream
segment, which can be further subdivided into left and right HBs
(Fig. b). A low value of the contributing (FA)
area t results in a dense hydrological network draining a large number of
small HBs, and a large value of t results in a reduced number of streams
draining a smaller number of relatively large HBs.
At each iteration, where a GIS layer showing APs is
available, r.slopeunits identifies the grid cells in the APs and
excludes them from the analysis (Fig. c). When the SUs are
exploited for the analysis of the processes causing slope instability, the
exclusion is justified by the empirical observation that landslides do not
occur in plain areas. The value of the areamin parameter a
defines the smallest possible (planimetric) area for a SU. The circular
variance is defined as 1-|R|/Nv, in the range between 0 and 1,
where Nv is the number of grid cells in each HB and |R| is the
magnitude of the vector R that results from the sum of all unit
vectors describing the orientation of each grid cell. As an example,
Fig. a shows that a group of unit vectors dispersed 23∘
apart, on average, is characterized by a circular variance of 0.1, and
Fig. b shows that a group of unit vectors dispersed 62∘
apart, on average, is characterized by a circular variance of 0.6. Thus, a
value of 0.1 of the circular variance represents grid cells all facing nearly
in the same direction, whereas a value of 0.6 represents more dispersed
grid cells. In the algorithm, the circular variance is controlled by the
value of the cvmin parameter c, affecting the homogeneity of
terrain aspect in the HBs. Small values of c result in more uniform HBs, and
large values of c in less uniform HBs, in terms of terrain aspect.
Graphical representation of the circular variance of terrain aspect,
1-|R|/Nv. Two groups of unit vectors are shown. The unit vectors
represent the local direction of terrain aspect for each grid cell, resulting
in circular variance (a) of 0.1 and (b) of 0.6. Unit
vectors are perpendicular to the local topography, represented by the
grid cell.
At each iteration, r.watershed splits each existing parent
half basin, HBparent (Fig. d) into nested
child half basins, HBchild. The average area of the
HBchild defined for each HBparent is checked against a.
When the average area is smaller than a, the subdivision is rejected and
the HBparent is selected as a candidate SU. When the average area
is larger than a, the procedure keeps the HBchild for the next
step of the analysis. The rejection procedure prevents very small HBs from
being selected as a candidate SU.
The next step of the procedure consists in comparing the size and circular
variance of each HBchild with the user-defined values a and c.
Where the circular variance is smaller than c, or the size is smaller than
a, the HBchild is taken as a candidate SU (Fig. e).
If the user defines the optional input parameter maxarea, the
control on the circular variance is not performed for the HBchild
having a size larger than maxarea. This imposes a constraint on the
maximum size of the candidate SU (not shown in Fig. e). Each and
every remaining HBchild is fed to the next iteration of
r.watershed, which is initialized using a smaller value of t. At
the ith iteration, the value of t depends on the value of the reduction
factor r, according to ti+1=ti-ti/r (Fig. f).
The decrease of ti is faster for small values of r≥2. We checked
empirically that values of r>10 lead to visually
better results, at least in our study area. This is due to the fact that a
slow decrease of ti allows for a better (finer) control on the subdivision
of the parent half basin, HBparent. On the other hand, a fast
decrease obtained with r=2 prevents the algorithm from checking if
intermediate values of ti produce a candidate SU. Thus, a slow decrease in
ti results in a larger number of iterations, which produce better results
at the expenses of a longer computing time required to complete the
iterations.
At each iteration, each HBchild is processed again by
r.watershed as HBparent. The iterative procedure ends when
the entire study area is subdivided into candidate SUs that match the user
requirements, in terms of minimum area (a) and circular variance (c). In
the resulting map, the size and shape of the candidate SUs can be determined
by the constraint of minimum surface area, or by the constraint of the
minimum circular variance of the terrain aspect. The final terrain
subdivision contains candidate SUs whose minimum size approximates a.
The final SU partitioning is obtained after an additional (cleaning) step
intended to identify and process candidate SUs exhibiting unrealistic or
unacceptable size or shape (Fig. g). This is discussed in the
next section.
Slope units cleaning procedure
The r.slopeunits software may produce locally unrealistic candidate
SUs which are too small, too large, or oddly shaped. As an example, in large
open valleys where terrain is flat or multiple channels join in a small area,
unrealistically small subdivisions can be produced. Another example is
represented by unrealistically elongated or large candidate SUs found along
regular and planar slopes. These terrain subdivisions, although legitimate
from the algorithm hydrological perspective, are problematic for practical
applications and should be revised and removed eventually. Very small
candidate SUs consisting of a few grid cells are often the result of artifacts
(errors) in the DEM. These candidate SUs should also be removed. To remove
candidate SUs with unrealistic or unwanted sizes (Fig. g), we have
implemented three distinct software tools based on three different methods.
The three methods require the user to set the cleansize parameter
that imposes a strict constraint on the minimum possible size (planimetric
area) for a slope unit.
The first method simply removes all candidate SUs smaller than
cleansize. The adjacent candidate SUs are enlarged to fill the area
left by the removed units, using the r.grow GRASS GIS module. The
second method, in addition to removing all candidate SUs smaller than
cleansize, also removes odd-shaped polygons from the set of the
candidate SUs. Enabled via the -m flag in combination with
cleansize, the second method removes markedly elongated candidate
SUs with a width smaller than two grid cells. The third method merges small
candidate SUs with neighboring ones based on the average terrain aspect.
Enabled via the -n flag in combination with cleansize, the
third method calculates the average terrain aspect of all the grid cells in
each small candidate SU. The average aspects of the neighboring SUs are
compared, and the two adjacent units exhibiting the smallest difference in
average terrain aspect are merged, provided that the SU that is removed
shares a significant part of its boundary with the neighboring unit. The
final result is a terrain subdivision in which the vast majority of the SU
has an area larger than cleansize. A drawback of the third method is
that it is significantly more computer intensive than the other two methods,
requiring longer processing times.
Segmentation metric
To evaluate the terrain partitioning into SUs, we use a simple metric
originally proposed for the evaluation of the quality of a segmentation
result . In digital image processing, segmentation
consists in the process of partitioning an image into sets of pixels, such
that pixels within the same set share certain common characteristics. Here,
we consider the terrain aspect grid map as an image to be segmented, and we
assume that the segmentation metric proposed by is
appropriate to evaluate the terrain partition into SUs. We base the assumption
on the observation that the metric makes a straightforward evaluation of the
internal homogeneity of the SUs using the local aspect variance V, and the
external heterogeneity of the SUs using the autocorrelation index, I. The
two quantities are defined as follows:
V=∑nsncn∑nsn,
and
I=N∑n,lwnl(αn-α‾)(αl-α‾)(∑n(αn-α‾)2)∑n,lwnl,
where n labels all the N SUs in a given partition, sn is the surface
area of the nth SU, cn is the circular variance of the aspect in the
nth SU, αn is the average aspect of the nth SU,
α‾ is the average aspect of the entire terrain aspect map,
and wnl is an indicator for spatial proximity, equal to unity if SU n
and l are adjacent, zero otherwise. The local variance V, defined in
Eq. (), assigns more importance to large SUs, avoiding numerical
instabilities produced by small SUs. The autocorrelation index I of
Eq. () has minima for partitions that exhibit well-defined
boundaries between different SUs.
The optimal selection of the input parameters is the one that combines small V and small
I. This is quantified by the following objective function :
F(V,I)=Vmax-VVmax-Vmin+Imax-IImax-Imin,
where Vmin(max) and Imin(max) are the minimum (maximum) values
of the quantities in Eqs. () and () as a function of the
input parameters. To calculate I, we rewrite Eq. () to make it
consistent with the terrain aspect map. The aspect map contains values in
degrees, and the average values and products cannot be taken
straightforwardly, and the following definitions have to be considered. The
average values of the angles are a vectorial sum of unit vectors, so that
α¯=Arctan∑jsinαj∑jcosαj,
where the index j runs over all the grid cells in the terrain aspect map. A
similar definition holds for αi, the average aspect inside the ith
slope unit, if the sum in Eq. () is limited to the grid cells
belonging to the ith SU. The difference (αi-α¯) should
also be intended vectorially, as follows:
αi-α¯=Arctansinαi-sinα¯cosαi-cosα¯.
Lastly, the product at the numerator of Eq. () is taken as the
scalar product of the vectors (αi-α¯) and (αj-α¯), as follows:
(αi-α¯)⋅(αj-α¯)=cosθicosθj+sinθisinθj,
where
θi=Arctansinαi-sinα¯cosαi-cosα¯,θj=Arctansinαj-sinα¯cosαj-cosα¯.
Care must be taken in expressing angles and arcs consistently in degrees or
radians.
The segmentation metric F(V,I) is a measure of the degree of fulfillment of
the SU internal homogeneity requirement, and it is related only to the SU
geometrical and morphological delineation. The metric can be used to define
the optimal (best) partition of the territory in terms of aspect
segmentation by maximization of F(V,I)=F(V(a,c),I(a,c)) as a function of
the a and c user-defined modeling parameters.
Landslide susceptibility modeling
Landslide susceptibility (LS) is the likelihood of landslide occurrence in an
area, given the local terrain conditions, including topography, morphology,
hydrology, lithology, and land use
. Various types of LS modeling
approaches are available in the literature. The approaches differ – among
other things – on the type of the TU used to partition the landscape and to
ascertain LS .
Interestingly, instead of trying to define where landslides are not expected,
e.g.,, over the last decades a lot of efforts have
been spent on the prediction of the spatial probability of the slope
failures. Among the many available types of TUs , SUs have
proved to be effective terrain subdivisions for LS modeling.
To model LS, we considered slow- to very slow-moving shallow slides,
deep-seated slides, and earth flows, and we excluded rapid to fast-moving
landslides, including debris flows and rock falls. The r.slopeunits
software performs the delineation of the SUs, and does not perform the LS
modeling. For the latter, we exploit specific modeling software
.
In this work, we prepare LS models adopting a single multivariate statistical
classification model. For the purpose, we use a logistic regression model
(LRM) to quantify the relationship between dependent (landslide
presence/absence) and independent (geo-environmental) variables. We use the
presence/absence of landslides in each SU as the grouping (i.e., dependent)
variable. Adopting a consolidated approach in our study area
, SUs with 2 % or more of
their area occupied by landslides are considered unstable (having
landslides), and SUs with less than 2 % of the area occupied by landslides
are considered stable (free of landslides). The 2 % threshold value
depends on the accuracy of a typical landslide inventory map
. Users of the
r.slopeunits software may select a different value for the landslide
presence/absence threshold in the LRM (or any other classification model,
where considered more appropriate, in different study areas, and with
different input data. Numerical (i.e., terrain elevation, slope, curvature,
and other variables derived from the DEM), and categorical (i.e., lithology
and land use) variables are used as explanatory (i.e., independent) variables
in the LS modeling. Each SU is characterized by (i) statistics calculated
for all the numerical variables, and (ii) percentages of all classes for
the categorical variables.
The LS evaluation is repeated many times using different SU terrain
subdivisions obtained changing the r.slopeunits (a,c) modeling
parameters, and cleaned from small areas using the first (and simplest)
method described in Sect. . We evaluate the performance
skills of the different LS models calculating the AUCROC. ROC curves show the performance of a binary classifier
system when different discrimination probability thresholds are chosen
. A ROC curve plots the true positive rate (TPR) against
the false positive rate (FPR) for the different thresholds. The area under
the ROC curve, AUCROC, ranging from 0 to 1, is used to measure the
performance of a model classifier that, in our case, corresponds to the LS
model.
Hereafter, we quantify the AUCROC metric with the R(a,c)
function, for each value of the a (surface area) and c (circular
variance) input parameters of the r.slopeunits software. We stress
that we use the AUCROC metric to evaluate the fitting performance
of the LS model, i.e., to evaluate the ability of the LS model to fit the same
landslide set used to construct the LS model (the landslide training set),
and not an independent landslide validation set
. This is done purposely, because the purpose
of the procedure is not to evaluate the performance of the LS classification
but to help determine an optimal terrain subdivision for LS modeling, and
thus before any LS model is available for proper validation. When an optimal
SU subdivision is obtained (see Sect. ), and a
corresponding LS model is prepared, the prediction skills of the model can be
evaluated using independent landslide information (where this is available)
.
In addition to the AUCROC, which is a direct measure of the
fitting/prediction performance of a binary classifier, the performance of the
LRM model can be analyzed in terms of how the different input variables (both
numerical and categorical) contribute to the final result
. In the model, a p value can be associated to each
variable, and used to establish the significance of the variable in the LRM.
The fraction of significant variables used by the LRM can be used to
qualitatively understand the behavior of the classification model as a
function of the r.slopeunits software input parameters or, in turn,
as a function of the average size of the SUs.
Optimization of SU partitioning for LS zonation
Once, for all the SU sets computed using different modeling parameters
(i.e., different a (surface area) and c (circular variance) values),
(i) the SU terrain aspect segmentation metric F(a,c) – that assesses how
well the requirements of internal homogeneity/external heterogeneity are
fulfilled – has been established (2a in Fig. and
Sect. ; ); and (ii) the performance of
the individual LS models are estimated using the AUCROC metric
R(a,c) – that assesses the calibration skills of the LRM used for LS
modeling – has also been established (2b in Fig. and
Sect. ; ), a proper objective function S
that combines the aspect segmentation metric (F(a,c)) and the
AUCROC calibration metric (R(a,c)) is established. Maximization
of S(a,c) as a function of the a (the minimum surface area of the
slope unit) and c (the slope unit circular variance) modeling parameters
allows to single out the optimal SU terrain subdivision for LS modeling in
the given study area.
The reason for proposing a combination of the aspect segmentation and the AUCROC metrics
in the search for an optimal terrain subdivision for LS modeling is the following.
The single segmentation metric F(a,c) is a measure of the degree of fulfillment
of inter-unit homogeneity and intra-unit heterogeneity for a SU delineation obtained with
given (a, c) values. As such, F(a,c) is related only to the geometrical delineation of the
SUs, and does not consider the subsequent application of a LS model, the presence/absence
of landslides, or any quantity other than terrain aspect.
(a) Shaded relief image of the study area located on the
upper Tiber River basin, Umbria, central Italy. Shades of green to brown show
increasing elevation. Inset shows location of the study area in Italy.
(b) Landslide inventory map . Inset shows the
detail of the landslide mapping. Landslides (shown in red) were used to
prepare the landslide susceptibility zonations shown in Fig. .
The maps are in the UTM zone 32, datum ED50 (EPSG:23032) reference system.
To combine the two functions R(a,c) and F(a,c) into a single objective function,
we normalized them to [0,1] as follows:
Ro(a,c)=R(a,c)-Rmin(a,c)Rmax(a,c)-Rmin(a,c)Fo(a,c)=F(a,c)-Fmin(a,c)Fmax(a,c)-Fmin(a,c).
The functions Ro(a,c) and Fo(a,c) are then multiplied to obtain the
final objective function S(a,c):
S(a,c)=Ro(a,c)Fo(a,c),
which embodies information on the quality of the terrain aspect map
segmentation and on the performance of the LS model in a consistent,
objective, and reproducible way. The function S(a,c) assumes values in the
range [0,1]: the larger the value the better the SU partitioning in terms
of (i) SU internal homogeneity and external heterogeneity, and
(ii) suitability of the subdivision for LS zonation in our study area.
Test area
We tested our proposed modeling framework for the delineation of SUs, and for
the selection of the optimal modeling parameters for LS assessment, in a
portion of the upper Tiber River basin, central Italy (Fig. a).
In the 2000 km2 area, elevation ranges from 175 to 1571 m, and terrain
gradient from almost zero along the river plains, to more than 70∘ in
the mountains and the steepest hills. Four lithological complexes, or groups
of rock units , crop out in the area, including:
(i) sedimentary rocks pertaining to the Umbria–Marche sequence, Lias to
lower Miocene in age; (ii) rocks pertaining to the Umbria turbidites
sequence, Miocene in age; (iii) continental, post-orogenic deposits, Pliocene
to Pleistocene in age; and (iv) alluvial deposits, recent in age. Each
lithological complex comprises different sedimentary rock types varying in
strength from hard to weak and soft rocks. Hard rocks are massive limestone,
cherty limestone, sandstone, travertine, and conglomerate. Weak rocks are
marl, rock-shale, sand, silty clay, and stiff over-consolidated clay. Soft
rocks are clay, silty clay, and shale. Rocks are mostly layered and locally
structurally complex. Soils in the area reflect the lithological types, and
range in thickness from less than 20 cm where limestone and sandstone crop
out along steep slopes, to more than 1.5 m in karst depressions and in large
open valleys.
(a) Lithological map of upper Tiber
River basin, Umbria, central Italy .
Details of the lithological types are given in Table .
(b) Land use map of the study area.
Legend: AE: urban area, AN: bare soil, AQ: water,
BO: forest, CA: orchard, CO: olive grove, CV: vineyard, LP: poplar trees,
NN/NX: unclassified, PA: meadow/pasture, SA: treed seminative, SS: simple
seminative.
The maps are in the UTM zone 32, datum ED50 (EPSG:23032) reference system.
To model LS, we use a digital representation of the terrain elevation, an
inventory of known landslides, and relevant geo-environmental information. We
use a DEM with a ground resolution of 25 m × 25 m obtained through
linear interpolation of elevation data along contour lines shown on
1 : 25 000 topographic base maps
(Fig. a). The landslide inventory (Fig. b) was
obtained from the visual interpretation of multiple sets of aerial
photographs flown between 1954 and 1977, aided by field surveys, review of
historical and bibliographical data, and geological, geomorphological, and
other available landslide maps
. To prepare the LS
model, we considered only the shallow slides, the deep-seated slides, and the
earth flows. These landslides are (i) slow- to very slow-moving failures, and
(ii) they typically remain in the slope (i.e., the slope unit) where they
occur. For the deep-seated landslides and the earth flows, the landslide
source (depletion) area and the deposit were considered together. This is a
standard approach in modeling LS for these types of landslides. We excluded
from the LS modeling all the rapid to fast-moving landslides, including
debris flows and rock falls that may travel outside the slope (i.e., the
slope unit) where they form.
We obtained lithological information (Fig. a) from available
geological maps, at 1 : 10 000 scale , prepared in
the framework of the Italian national geological mapping project CARG and in
other regional geological mapping projects. The original maps, in vector
format, were edited to eliminate and reclassify polygons coded as landslide
deposits or debris flow deposits, and to reclassify the original 186 geologic
formations and 20 cover types in five lithological complexes or lithological
domains (Table ). Definition of the five lithological complexes
was made on the basis of the characteristics of the rock types (carbonate,
terrigenous, volcanic, post-orogenic sediments) and the degree of competence
or composition of the different geological units (massive, laminated
sandstone/pelitic-rock ratio). Applying these criteria, the original 206
geological units were grouped in 17 lithological units. We obtained
information on land cover from a map, at 1 : 10 000 scale
, prepared through the visual interpretation of color
aerial photography at 1 : 13 000 scale, acquired in 1977
(Fig. b). The map contains 13 land cover classes, of which the
most common are forest (42 %), arable land (31 %), meadow and pasture
(10 %), built up areas (10 %), and vineyards, live trees, and orchards
(6 %).
Lithological codes used in Fig. . SD is sandstone,
P is pelitic rock,
CO is conglomerate, S is sand, G is clay .
A group of 9 (out of 99) SU terrain subdivisions for a portion
of the study area. The SUs were obtained changing the a
and c parameters used by the r.slopeunit software.
The maps are in the UTM zone 32, datum ED50 (EPSG:23032) reference system.
The study area (Fig. ) corresponds to an alert zone used by the
Italian National Department for Civil Protection to issue landslide (and
flood) regional warnings. The boundary of the alert zone is partly
administrative, and does not correspond locally to drainage and divides
lines. As a result, our SU partitioning intersects locally the boundary of
the alert zone. For convenience, for our analysis we considered only SUs that
fall entirely within the alert zone. As a drawback, the extent of the study
area varies slightly depending on the combination of the selected a and c
parameters. We maintain that this has a negligible effect on the final
modeling results.
ResultsSlope units delineation
In the study area, we ran the r.slopeunits software for 99 different
combinations of user-defined input parameters, resulting in 99 different
terrain subdivisions. In the iterative procedure (Fig. ), the
initial FA threshold (t) area and the reduction factor (r) control the
numerical convergence, and do not have an explicit geomorphological meaning.
On the other hand, the minimum area (a) and the circular variance (c)
determine the size and control the aspect of the SUs. For the analysis, we
selected a large value for the FA area (t=5×106 m2) keeping
it constant for all the different model runs. The large value was chosen to
obtain large initial HBs that could be further subdivided into smaller SUs by
the iterative procedure (see Sect. ). The value is also
consistent with (i.e., substantially larger than) (i) the size of the average
SU used to partition the same area in a different LS modeling effort
, and (ii) the average area of the
considered landslides (shallow slides, the deep-seated slides, and the earth
flows) in the study area . Selection of the reduction
factor (r=10) was heuristic and motivated by the fact that this figure
provided stable results compared to those obtained using larger values. The
two most relevant parameters, the minimum area a and the circular variance
c, were selected from broad ranges: a= 10 000, 25 000, 50 000,
75 000, 100 000, 125 000, 150 000, 200 000, and 300 000 m2, and
0.1 <c< 0.6, at evenly spaced values with an increment of 0.05.
For all the r.slopeunits model runs, we used the same value for
cleansize= 20 000 m2, to remove candidate SUs with area
< 20 000 m2 using the first (and simplest) of the three methods
described in Sect. .
Figure shows 9 of the 99 results of the terrain subdivisions
obtained using different combinations of the a and c modeling
parameters. The map in the upper left (lower right) corner shows the finest
(coarsest) SU partitioning, determined using small (large) values of a and
c. The map in the center was obtained using intermediate values for the two
user-defined modeling parameters. For a limited portion of the study area,
Fig. shows different partitioning results. In particular,
Fig. a and b show the overlay of the three different partitions
with the landslide inventory map (Fig. ), using a two- and
three-dimensional visualization, respectively, and a shaded image relief of the
terrain, whereas Fig. c, d, and e show separately the same
partitions using a three-dimensional representation. Visual inspection of
Fig. a, b, and c reveals that the coarser subdivision
(c= 0.60 and a= 0.3 km2), shown in blue, defines large SUs
characterized by heterogeneous orientation (aspect) values. On the other
hand, the finest SU subdivision (shown in green in Fig. a, b and
e) obtained using c= 0.10 and a= 0.01 km2, is too small to
completely include many of the landslides (shown in yellow). The combination
that uses intermediate values c= 0.35 and a= 0.15 km2
resulted in the SU subdivision shown in red in Fig. a, b, and d.
Example of subdivisions into SUs for a portion of the
study area.
Legend: blue, red, and green lines show boundaries of SUs of increasing
density and corresponding decreasing average size. Yellow areas are
landslides. The five maps show the same area in plan
view (a) and in perspective view (b, c, d, e).
Figure shows the effect of different combinations of a and c
on the average SU size. The average area of the SU increases significantly
with c (less homogeneous, more irregular slope), and it is less sensitive
to the increment of a (Fig. a). The effect of c becomes
predominant in Fig. b. The standard deviation of the area of the
SU varies significantly with c, highlighting that larger values of c
increase the average and the variability of the SU size (Fig. a
and b, respectively).
(a) Average and (b) standard deviation of the size
of the SUs, for different
combinations of a and c parameters.
The minimum size of the SUs is fixed by the a parameter, and the
maximum size of the SUs is independent of a.
Segmentation metric
For each of the 99 terrain subdivisions obtained using the procedure
described above, we calculated the segmentation objective function value
given by Eq. (). The segmentation metric F(a,c)
(Fig. ) is a measure of the performance of our SU delineation
algorithm, and an assessment of how well the requirements of internal
homogeneity/external heterogeneity are fulfilled by the procedure, as a
function of a and c (2a in Fig. , Sect. ).
Where the SUs are relatively small, their degree of internal homogeneity is
large, but the requested heterogeneity between adjacent units is not
completely fulfilled. Where the SUs are large, the requested internal
homogeneity is not fulfilled entirely, because in each SU the aspect
variability is large. The analysis of the F(a,c) values in
Fig. suggests that SU subdivisions obtained using c smaller
than about 0.2 and a smaller than about 50 000 m2, or c larger than
about 0.5, should not be considered in the analysis because they are too
small or too large to satisfy the aspect variability requirement.
Segmentation objective function values (Eq. ) calculated
for 99 SU partitions obtained using different combinations of the a and c
parameters.
Landslide susceptibility modeling
For each of the 99 SU delineations, we prepared a different LS zonation using
a LRM (Sect. ) adopting the modeling
scheme described by . Figure shows
the results obtained for 9 (out of 99) combinations of the a and c
parameters. For each of the 99 susceptibility assessments, we evaluated the
fitting (calibration) performance of the models computing AUCROC, and Fig. shows the obtained AUCROC
as a function of the a and c parameters (Sect. ).
The larger values of AUCROC were obtained for LS zonations based on
SU partitions resulting from large values of c and a. Such combinations
may locally result in SUs with extremely large internal heterogeneity.
Signatures of the heterogeneity within very large slope units can be found
both in the segmentation metric and in the LRM model results. In the
segmentation metric case, this is very straightforward since the values of
F(a,c), which is a direct measure of the slope aspect homogeneity within
SUs, clearly decrease with increasing values of a and c, as shown in
Fig. . Very large SUs, however, are not only heterogeneous in
terms of terrain aspect, but also in terms of the morphometric and thematic
variables used as input of the LRM. This is reflected in the number of input
variables that significantly contribute to the susceptibility model results
as a function of a and c. We computed the number of statistically
significant variables in each realization of the LRM (i.e., the variables
with a p value < 0.05). Figure shows that the number of
significant variables ranges from 5 % (of the 50 morphometric and
thematic variables) for large SUs, to 35 % for small SUs. From this
analysis we observe that for very large slope units, only very few variables
are effectively used by the LRM. A more detailed analysis reveals that, in
our test case, lithological variables significantly control the results,
whereas other local settings (e.g., terrain slope) are neglected. The relevant
variables are typically the terrigenous sediments and carbonate lithological
complexes, where landslides are expected and not expected, respectively. As a
result, in the region of large (a,c) parameters, even if we obtain high
values of AUCROC, the LRM can be replaced by a simple heuristic
analysis of the lithological map. The fine details of the remaining input
variables are lost and a multivariate statistical approach is of little use.
We clarify that to evaluate the model performance, any statistical metric
based on the comparison of observed and predicted data (e.g., confusion
matrices and derived indexes), would exhibit the same or similar trend as the
AUCROC as a function of the SU size.
The group of 9 (out of 99) LS maps obtained with different
SU partitions resulting from different combinations of the
a and c parameters.
The maps are in the UTM zone 32, datum ED50 (EPSG:23032) reference system.
Discussion
We have run the r.slopeunits software with a significant number of
combinations (99) of the (a, c) input parameters, and a corresponding
number of realizations of the LS model. Results showed that new
r.slopeunits software was capable of capturing the morphological
variability of the landscape and partitioning the study area into SU
subdivisions of different shapes and sizes well suited for LS modeling and
zonation. As a matter of fact, depending on the type of landslides, the scale
of the available DEM, the morphological variability of the landscape, and the
purpose of the zonation, the detail of the terrain subdivision may vary. A
detailed terrain partitioning, with many small SUs, is required to capture the
complex morphology of badlands, or to model the susceptibility to small and
very small landslides (i.e., soil slips). A coarse terrain subdivision is best
suited for modeling the susceptibility of very old and very large,
deep-seated, complex and compound landslides. Coarse subdivisions can also be
used to model the susceptibility to channeled debris flows that travel long
distances from the source areas to the depositional areas. Subdivisions of
intermediate size may be required for medium to large slides and earth flows
. By tuning the set of user-defined model parameters,
r.slopeunits can prepare SU terrain subdivisions for LS modeling in
different geomorphological settings.
Concerning the LS model, we acknowledge that our selection of the 2 %
presence/absence threshold may influence the production of the appropriate SU
subdivision, and may affect the results of the LS zonation. Examination of
different thresholds is not investigated in the present work, because it is
not an input parameter of the r.slopeunits software and does not
change the logic of the approach or the rationale behind our optimization
procedure.
Values of the AUCROC
calculated for LS maps estimated using SU
partitions derived for different combination of the a and c user-defined
modeling parameters.
Percentage of relevant variables in the LRM
used in this work to prepare the LS maps
as a function of the a and c user-defined modeling parameters.
Combination of a and c are the same used to prepare Fig. .
Note that the direction of the axes is reversed with respect to Fig. .
(a)Ro(a,c) (blue) and Fo(a,c) (red) functions,
defined by Eqs. () and (). (b)So(a,c)
function defined by Eq. ().
The functions were interpolated on a denser mesh for improved visual representation.
We clarify that the subdivisions produced by r.slopeunits using
different (a,c) parameters are nested, i.e., the boundaries of a coarse
resolution subdivision encompass the boundaries of intermediate and finer
subdivisions (see Fig. c, d, e). This is a significant
operational advantage where landslides of different sizes and types coexist,
posing different threats and requiring multiple and combined susceptibility
assessments, each characterized by a different terrain subdivision
. Optimal values of the (a,c) parameters have to be
determined to obtain the best SU subdivision for a particular goal, in our
case, LS modeling. We defined a custom objective function S(a,c) to
determine such optimal values. S(a,c) is the product of a segmentation
quality measure, F(a,c), and LS model performance in calibration, R(a,c).
If only the F(a,c) metric is used to select a particular set of modeling
parameters, the resulting optimal (best) set of SUs has the only meaning
of “best partition of the territory in terms of aspect segmentation”.
Similarly, the R(a,c) metric considers solely the classification results of
the LS model and not the geometry of the single SU, some of which may be
inadequate (e.g., too large, too irregular, too small) for the scope of the
terrain zonation. Values of F(a,c) indicate that there are combinations of
the c and a parameters that result in SU subdivisions that do not satisfy
the user requirements in terms of SU internal homogeneity and external
heterogeneity (Fig. ) (Sect. ). On the other hand,
the AUCROC metric increases with the average size of the SU
(Fig. ) (Sect. ). To select the optimal terrain
partitioning for LS zonation in our study area, we exploit the objective
function S(a,c), which simultaneously quantifies
(Sect. ): (i) the SU internal homogeneity and external
heterogeneity (Fig. a), and (ii) the (fitting) performance of the
LS model (Fig. a). Maximization of S(a,c) (Fig. b)
provides the best combination of the (a,c) modeling parameters for a
terrain subdivision optimal for LS modeling in our study area.
The SU subdivision corresponding to the best parameters
selected by our optimization procedure. The values of the parameters
are a= 150 000 m2, a= 0.35. The associated LS result
is shown in Fig. , in the central box, corresponding
to the optimal parameters values.
In addition to the AUCROC, we have analyzed the performance of the
LRM model by studying the fraction of significant variables used by the LRM,
to qualitatively understand the behavior of the classification model as a
function of the r.slopeunits software input parameters or, in turn,
as a function of the average size of the SU. The LRM is expected to use the
input data less efficiently when the average SU size grows, resulting in a
smaller number of significant input variables, which is indeed what we
observed. This is due to the LRM inability to discriminate between input
variables when the SUs are too large, since each unit usually contains all the
possible values of the variables. Using less data makes it easier for the LRM
model to produce a high AUCROC result, which does not necessarily
correspond to the optimal SU set. The complication is removed using the
S(a,c)=Fo(a,c)Ro(a,c) function, whose F(a,c) component prevents
unrealistic SU sets (both large and small) to have a high overall score.
The function S(a,c) (Fig. b), calculated in our test case for
different combinations of the a and c modeling parameters, has a maximum
value at a= 150 000 m2 and c= 0.35. The set of SUs that
corresponds to the optimal combination of the modeling parameters can be
singled out as our optimal (best) result. The LS results corresponding to
the optimal combination were already shown in the central box of
Fig. , and the optimal SU map is presented in Fig. .
Conclusions
Despite the clear advantages of SUs over competing mapping units for LS
modeling , inspection of the literature reveals that
only a small proportion (8 %) of the LS zonations prepared in the last
three decades worldwide was performed using SUs . The
limited use of SUs for LS modeling and zonation is due to (among other factors) the unavailability
of readily available, easy-to-use software for the
accurate and automatic delineation of SUs, and to the intrinsic difficulty in
selecting a priori the appropriate size of the SUs for proper terrain
partitioning in a given area.
To contribute to filling this gap, we developed new software for the automatic
delineation of SUs in large and complex geographical areas based on terrain
elevation data (i.e., a DEM) and a small number of user-defined parameters.
We further proposed and tested a procedure for the optimal selection of the
user parameters in a 2000 km2 area in Umbria, central Italy.
We expect that the r.slopeunits software will be used to prepare
terrain subdivisions in different morphological settings, contributing to the
preparation of reliable and robust LS models and
associated zonations. We acknowledge that further work is required to
investigate the optimization of SU partitions for different statistically
based tools used in the literature for LS modeling and zonation (e.g.,
discriminant analysis, neural network). have argued that
lack of standards hampers landslide studies. This is also the case for the
production of landslide susceptibility models and associated maps. We expect
that systematic use of the modeling framework proposed in this work
(Fig. , Sect. ) and of the r.slopeunits
software for the objective selection of the user-defined modeling parameters,
will contribute to the production of more reliable landslide susceptibility
models. It will also facilitate the meaningful comparison of landslide
susceptibility models produced, e.g., in the same area using different
modeling tools, or in different and distant areas using the same or different
modeling tools.
Finally, we argue that the proposed modeling framework and the
r.slopeunits software are general and not site- or process-specific,
and can be used to prepare terrain subdivisions for scopes different from
landslide susceptibility mapping, including, e.g., definition of rainfall
thresholds for possible landslide initiation, distributed hydrological
modelling, statistically based inundation mapping, and the detection and
mapping of landslides and other instability processes from satellite imagery.
Code availability
The code r.slopeunits is a free software under the GNU General
Public License (v2 and higher). Details about the use and redistribution of the software can be
found in the file https://grass.osgeo.org/home/copyright/ that comes
with GRASS GIS. The software and a short user manual can be downloaded at
http://geomorphology.irpi.cnr.it/tools/slope-units
().
Notation
In Table , we list the main variables and the acronyms used
in the text.
Main variables and acronyms used in the text.
VariableExplanationFirst introducedDimensionsaminimum surface area for the SUsSect. m2cminimum circular varianceSect. –rreduction factorSect. –tflow accumulation thresholdSect. m2IAutocorrelation indexEq. ()–VLocal aspect varianceEq. ()–F(V,I)Aspect segmentation metric, also F(a,c)Eq. ()–R(a,c)AUCROC metric for LRM calibrationSect. –S(a,c)Combined segmentation & AUCROC metricEq. ()–AcronymExplanationAPAlluvial plainAUCArea under the curveDEMDigital elevation modelFAFlow accumulationFPRFalse positive rateGISGeographical information systemHBHalf basin (left and right portion of a slope unit)LRMLogistic regression modelLSLandslide susceptibilityMFDMultiple flow directionROCReceiver operating characteristicSFDSingle flow directionSUSlope unit, a morphological terrain unitbounded by drainage and divide linesTPRTrue positive rateTUTerrain unit, a subdivision of the terrain
The Supplement related to this article is available online at doi:10.5194/gmd-9-3975-2016-supplement.
Acknowledgements
This work was supported by a grant of the Italian National Department of Civil
Protection, and by a grant of the Regione dell'Umbria under contract POR-FESR
(Repertorio Contratti no. 861, 22/3/2012). M. Alvioli was supported by a
grant of the Regione Umbria, under contract POR-FESR Umbria 2007–2013, asse
ii, attività a1, azione 5, and by a grant of the DPC. F. Fiorucci was
supported by a grant of the Regione Umbria, under contract POR-FESR 861,
2012. We thank A. C. Mondini (CNR IRPI) for useful discussions about
segmentation algorithms. Edited by: L.
Gross Reviewed by: two anonymous referees
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