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

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

SUs can be drawn manually from topographic maps of adequate scale and quality

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

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.

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

First, the

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 AUC

Lastly, an overall (combined) objective function is defined by properly combining
the segmentation (step 2a)
and the AUC

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.

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
AUC

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 AUC

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

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

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

Flowchart for the

The

The software adopts an iterative approach to partition a landscape into SUs.
In the first iteration,

At each iteration, where a GIS layer showing APs is
available,

Graphical representation of the circular variance of terrain aspect,

At each iteration,

The next step of the procedure consists in comparing the size and circular
variance of each HB

At each iteration, each HB

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.

The

The first method simply removes all candidate SUs smaller than

To evaluate the terrain partitioning into SUs, we use a simple metric
originally proposed for the evaluation of the quality of a segmentation
result

The optimal selection of the input parameters is the one that combines small

The segmentation metric

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

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

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

The LS evaluation is repeated many times using different SU terrain
subdivisions obtained changing the

Hereafter, we quantify the AUC

In addition to the AUC

Once, for all the SU sets computed using different modeling parameters
(i.e., different

The reason for proposing a combination of the aspect segmentation and the AUC

To combine the two functions

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.

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

We obtained lithological information (Fig.

Lithological codes used in Fig.

A group of 9 (out of 99) SU terrain subdivisions for a portion
of the study area. The SUs were obtained changing the

The study area (Fig.

In the study area, we ran the

Figure

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

Figure

For each of the 99 terrain subdivisions obtained using the procedure
described above, we calculated the segmentation objective function value
given by Eq. (

Segmentation objective function values (Eq.

For each of the 99 SU delineations, we prepared a different LS zonation using
a LRM (Sect.

The larger values of AUC

The group of 9 (out of 99) LS maps obtained with different
SU partitions resulting from different combinations of the

We have run the

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

Values of the AUC

Percentage of relevant variables in the LRM
used in this work to prepare the LS maps
as a function of the

We clarify that the subdivisions produced by

The SU subdivision corresponding to the best parameters
selected by our optimization procedure. The values of the parameters
are

In addition to the AUC

The function

Despite the clear advantages of SUs over competing mapping units for LS
modeling

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 km

We expect that the

Finally, we argue that the proposed modeling framework and the

The code

In Table

Main variables and acronyms used in the text.

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