The Gravitational Process Path (GPP) model can be used to simulate the process path and run-out area of gravitational processes based on a digital terrain model (DTM). The conceptual model combines several components (process path, run-out length, sink filling and material deposition) to simulate the movement of a mass point from an initiation site to the deposition area. For each component several modeling approaches are provided, which makes the tool configurable for different processes such as rockfall, debris flows or snow avalanches. The tool can be applied to regional-scale studies such as natural hazard susceptibility mapping but also contains components for scenario-based modeling of single events. Both the modeling approaches and precursor implementations of the tool have proven their applicability in numerous studies, also including geomorphological research questions such as the delineation of sediment cascades or the study of process connectivity. This is the first open-source implementation, completely re-written, extended and improved in many ways. The tool has been committed to the main repository of the System for Automated Geoscientific Analyses (SAGA) and thus will be available with every SAGA release.

Rapid mass movements such as rockfall, debris flows or snow avalanches are
common features in mountainous regions. Due to population growth and the
advancing construction of infrastructure and buildings in such areas, rapid
mass movements pose more and more of a risk to society and can result in severe
damages or even disasters. Besides early warning systems and protection
measures for disaster prevention, hazard susceptibility zoning, which
identifies potentially endangered areas, is required for risk analysis and
the creation of hazard maps

While physically based dynamic models can be used for detailed analyses of
single events

This paper introduces the Gravitational Process Path (GPP) model version 1.0, an attempt to provide a GIS-based modeling framework for the simulation of process path and run-out area of gravitational processes. The GPP model is a conceptual model, concatenating components for process path determination, run-out calculation, sink filling and material deposition. For each of these components, several well established modeling approaches are implemented and can be chosen by the user. This makes the GPP model configurable for different processes like rockfall, debris flows or avalanches.

Basically, the GPP model simulates the movement of a mass point over a raster
DTM from an initiation site to the deposition area. Therefore it includes
empirical, stochastic and physically based modeling approaches and provides
the option of terrain modification by material deposition during operation.
Although some of the implemented approaches are based on simplifying
concepts, realistic results can be achieved with the great advantage of
requiring only a few input parameters. This makes it possible to use the tool
for regional-scale studies, but it also includes some components for scenario
modeling of single events. The approaches implemented in the model components
have been successfully used for hazard susceptibility mapping

For process path modeling, the GPP model includes the single-flow-direction
path-finding approach of

For run-out distance calculation, the GPP model includes several approaches
based on the energy line principle

The GPP model is the first open-source implementation based on previous work
of the author, but it is completely reworked and enhanced in various aspects.
It is implemented as a tool for the System for Automated Geoscientific
Analyses (SAGA;

The paper is structured as follows: Sect.

The GPP model is intended to provide a software framework for gravitational process path modeling. It integrates components for process path determination, run-out calculation, sink filling and material deposition. For each of these components, several modeling approaches are implemented. This makes it possible to concatenate modeling approaches as required to simulate the behavior of a certain geomorphological process or to use suitable approaches with regard to the available input data.

Generally, the GPP model routes a mass point, here called a particle (following the nomenclature of physics engines), from an initiation site over a raster DTM to the deposition area. In the GPP model, these initiation sites are organized in so-called release areas, made up of one or more grid cells labeled as starting zones in an input raster data set. Such a raster data set has to be derived beforehand, usually by some kind of susceptibility modeling or (field) mapping.

The GPP model computes several model realizations for each start cell (Monte Carlo simulation). The number of model iterations is defined by the user (default: 1000 iterations). The overlay of the model results from all iterations shows the final model result, i.e., the complete process area (and not individual process paths), as every iteration will show a different result because of the stochastic components in the model.

Besides the components for process path and run-out calculation, the GPP model integrates components, which can modify the DTM in each model iteration by material deposition: there is a model component, which handles natural or artificial sinks, and a component to deposit material on process stop or along the process path. This allows the model to overcome sinks or to simulate the blocking of a channel by wood and debris. In order to use these components, the GPP model requires an input data set with material heights per start cell.

Figure

Flowchart of a basic GPP model configuration for modeling on a regional scale.

A model configuration including the filling of sinks is depicted in
Fig.

Flowchart of a GPP model configuration making use of the sink-filling approach.

Figure

Flowchart of a fully featured GPP model configuration for scenario modeling.

The sequence in which release areas, as well as particles, are initialized is
crucial when material deposition is simulated. The modification of
the terrain between model iterations can influence process paths and run-out
distances significantly. The following processing orders are implemented:

Release areas in sequence: the release areas are processed one by one; in each model iteration, all start cells of a release area are processed in ascending order of their elevation. This configuration computes all model iterations for the start cells of release area one, then for the start cells of release area two and so on.

Release areas in sequence per iteration: the release areas are processed one by one in each model iteration; the start cells are processed in ascending order of their elevation. This configuration computes a single model iteration with the start cells of release area one, then with all start cells of release area two and so on; the next model iteration is then run over all release areas.

Release areas in parallel per iteration: in each model iteration the start cells of all release areas are processed in ascending order of their elevation. With this configuration, all start cells are processed in each model iteration sorted by elevation, irrespective of their membership to a certain release area.

Depending on the overall configuration, the GPP model requires just a few parameters. These are either global parameters, used throughout the simulation, or (optionally) spatially distributed parameters provided as raster data sets. An example for the latter are spatially distributed friction values depending on factors such as surface characteristics or water content.

Within the following sections, the modeling approaches currently implemented
for each model component are described in detail. The user can choose which
model should be used in each component and combine them to simulate various
processes. Typical model configurations are presented in
Sect.

In order to determine the downslope process path of a particle from its initiation site, the GPP model implements two different approaches. One is a single-flow-direction algorithm, which selects that neighbor cell as next flow path cell to which the steepest downward slope is observed. The other, based on a random walk, is a multiple-flow-direction approach sensitive to the local slope conditions.

This approach, as proposed by

The model result is thus deterministic, with the exception of its behavior (as implemented in the GPP model) when two or more neighbor cells show the same steepest descent or when a flat area is reached. In the first case, one of the neighbor cells is chosen at random. On flat areas a set of potential neighbor cells is determined which is made up of all neighbors with the same elevation as the current cell which have not been traversed yet in the current model iteration. From this set, a process path cell is chosen at random. This introduces a probabilistic component. Further, the terrain could have been modified between two model iterations by sink filling or material deposition.

The

With this approach, the process path is modeled by a variant of the dfwalk
model as proposed by

For the currently processed grid cell, a set

The slope threshold makes it possible to adjust the model to different
topography: in steep sections of the process path, where the terrain slope is
near the threshold, only steep neighbors are allowed in addition to the
steepest descent. In flat sections, almost all lower neighbor cells are
potential flow path cells and the tendency for divergent flow is increased.
The degree of divergent flow below the slope threshold can be controlled by
the exponent of divergent flow. This sensitivity to the terrain conditions is
an important property which is missing in the modeling approaches developed
for hydrological processes, which distribute the flow proportionally to the
slope to all lower neighbors irrespective of the local topography

Finally, a cell is picked at random from the set

Effect of different random walk parameter settings;

In the GPP model, the approach is extended to also handle flat areas. This is
done as described for the

The result of several model iterations is a raster data set storing the
transition frequencies, i.e., how many times a grid cell has been traversed.
Figure

In Fig.

Figure

In order to determine the run-out length of a particle, several approaches are implemented in the GPP model. These range from rather simple but convenient approaches (regarding, for example, the comparison with field observations) based on the energy line principle to one- and two-parameter friction models. In the following, these approaches are described in detail.

The run-out length of a process is often described by the vertical and
horizontal distances covered by a particle from its start to the stopping
position:

The geometric gradient

For the Fahrböschung principle

Both the geometric gradient and the Fahrböschung principle do not
take into account that with rockfalls most of the initial energy is
dissipated once a rock impacts on the talus slope for the first time

The shadow angle can again be provided either as a global value or by a raster data set with shadow angles for each start cell. In order to determine the location of the first impact of a particle on the talus slope, the GPP model implements two different approaches: (i) the user provides a raster data set with impact areas. Once a particle reaches a cell labeled as impact area, the location of this cell is used to measure the shadow angle; (ii) a threshold describing the slope angle above which free fall is assumed is provided. As soon as the angle between the start cell and the current position of the particle drops below the threshold, the location of this cell is used to measure the shadow angle.

The one-parameter friction model has been developed to simulate rockfall and is
based upon concepts introduced by

energy reduction

where

preserved component of velocity

where

Approach (i) requires the user to specify the amount of energy reduction as
calibration parameter. Approach (ii) usually results in larger run-out distances. The strong
dependence of approach (ii) on the slope of the impact cell complicates the
model calibration

sliding:

where

rolling:

where

Once the velocity on a grid cell becomes zero, the end of the deposit is
reached. The model calibration usually requires only two parameters: the
amount of energy loss on impact (%) and, depending on the chosen mode of
motion, either the sliding or the rolling friction coefficient (–). The
friction coefficient can be provided as a global value or spatially distributed
by providing a raster data set with friction values. Impact on the talus
slope can be modeled either by providing an input raster data set with impact
areas or by using a slope threshold (see Sect.

The PCM model

The correction is based on the conservation of linear momentum and has a
higher magnitude in the event of abrupt transitions. The accurate stopping
position on a grid cell may be calculated by the following:

In the GPP model Eq. (

In the GPP model various deposition modeling approaches are implemented. In order to use these approaches, an input raster data set with material heights per start cell is required. This total material height is then averaged by the number of iterations to calculate the material height available for a particle in each iteration. Material that has not been spent in an iteration is made available for the remaining iterations. Deposited material immediately alters the terrain and the next iteration is computed on the modified DTM.

The most important deposition approach is the filling of sinks, which allows the GPP model to overcome small depressions or even larger obstacles like retention basins. Others simply deposit material once a particle stops or allow deposition along the process path based on slope and/or velocity thresholds. The latter can be used to model scenarios such as the blocking of a channel by wood or debris.

The sink-filling approach is immediately activated once a raster data set with material heights per start cell is provided as input. As soon as a sink is detected, the particle stops and material is deposited. The deposition approach attempts to preserve a downward slope if procurable, thus avoiding the creation of new sinks and making it possible to overcome the obstacle in subsequent model iterations.

The sink-filling approach is based on

This approach simply deposits material on the grid cell of the modeled
stopping position. The amount of material deposited on this cell is
controlled by the

The approach makes it possible to adjust the deposition behavior to different
geomorphological processes: simulating a rock fall event, the

Model configuration for rockfall modeling on a regional scale and
approximate parameter ranges (compiled from

The

The slope- and velocity-based approaches can be used separately or in combination. In the latter case, a deposition height is calculated with both approaches and the lower deposition height is applied. This reduces artefacts resulting from the usage of a single threshold. For example, on flat areas, no material is deposited as long as the velocity is still high.

The slope- and velocity-based approaches have a further parameter, the

A brief summary of the GPP model parameters and input and output data sets is
given in the Appendix: Table

Some applications of the GPP model on a regional scale are natural hazard
susceptibility mapping and the derivation of geomorphological process areas
and sediment cascades. It is possible to simulate different scenarios based
upon, for example, process magnitude, the existence of protection forest or
protection measures. The inclusion of the deposition model component is
usually only done on a more local scale. The modeling approaches available
for each model component make it possible to simulate different gravitational
processes depending on the overall model configuration. Within the following
sections typical model configurations and parameter settings are described
for rockfall, debris flow and avalanche modeling. Run-out calculations using
one of the approaches based on the energy line principle have been used for
all three process types, but as they are straightforward to use they are not
discussed in detail. A separate section provides further information on
scenario modeling. It must be noted that the parameter ranges provided for
each process have to be considered as approximate values only and are thought
to provide an initial guess. For example,

Coefficients of friction for different materials and land cover
(compiled from

Model configuration for debris flow modeling on a regional scale and
approximate parameter ranges (compiled from

A typical model configuration for rockfall modeling on a regional scale,
e.g., to create susceptibility maps, combines the modeling approaches shown
in Table

The threshold of free fall used in the

The model configuration thus requires the following raster data sets as input: a DTM, a raster with release areas and a raster with spatially distributed friction coefficients. Model outputs, describing the derived process area, are raster data sets storing the transition frequencies, the encountered maximum velocities and the stopping positions.

A typical model configuration for debris flow modeling on a regional scale is
shown in Table

Run-out distances are calculated on basis of the PCM model. The

The model configuration for avalanche modeling on a regional scale resembles
that for debris flow modeling, but the parameter variability is higher
because of the different properties of powder and wet snow avalanches (see
Table

Model configuration for avalanche modeling on a regional scale and
approximate parameter ranges (compiled from

Sink filling:

Scenario modeling usually addresses topics such as process magnitude, the impact
of protection forest or protection measures. Different process magnitudes are
usually modeled by using a different number of model iterations and/or
friction coefficients. For example, different friction coefficients can be
used to assess the relevance of protection forest by simulating events with
and without forest cover and to compare how the run-out distances increase

In order to demonstrate the approach for sink filling, a 10 m DTM has been
modified to include a sink along the process path. For the sake of
simplicity, the process path is modeled using the

Figure

Longitudinal profile illustrating the sink-filling approach:

Figure

The maximum velocities reached along the steeper parts of the process path
are almost the same (16 m s

Medium

Figure

Deposition modeling scenario on a high-resolution 2.5 m DTM:

The GPP model integrates several well known model approaches, which are
established in practice into a single GIS-based simulation framework. The
framework is highly modular, with components for process path, run-out
length, sink filling and material deposition. The GPP model is a conceptual
model, which provides the possibility to combine different modeling
approaches and thus to model different kinds of gravitational processes. The
currently implemented modeling approaches are not entirely physically based,
but build on empirical and basic principles to mimic typical macroscopic
characteristics of mass movements. Nowadays, several physically based
numerical simulation models are available

Although some modeling approaches included in the GPP model are based on rather simple concepts, it is their complex interaction which permits the delineation of the extent of gravitational process areas. Reasonable results can be obtained with a minimum of input data and model parameters, recommending the framework especially for susceptibility mapping on regional scales. Recent additions such as the model components for sink filling and deposition modeling make it also interesting for scenario modeling on various scales. Nevertheless, because of the limitations of the model it must be noted that this has to be done carefully on a local scale. For example, different block sizes of rockfall can only be simulated indirectly by using different friction parameters. Another limitation is the restriction of the process path routing to neighbor cells with equal or lower elevation, which makes the run-up of material on the opposite valley slope impossible. Like with every other simulation model it must be pointed out that it is a prerequisite to understand the functionality of the modeling approaches in detail before their application and the interpretation of the model results.

The GPP model provides only forward modeling capabilities. But as it is embedded in a GIS environment, model validation by observed historical events, e.g., by receiver operating characteristics (ROC curve), can be done outside the model. Also, the derivation of initiation sites can be done within the GIS environment. Currently lacking are tools to automatically estimate model parameters based on observed process areas. This would be a great addition.

Frameworks for the simulation of gravitational mass movements on a regional
scale have been released by various authors. For example,

The GPP model is written in C++ and implemented in the “Geomorphology” tool
library for the FOSS SAGA

Besides its purely scientific application, the GPP model also qualifies as
kind of sandbox game because of its characteristics. Dynamic processes are
reproduced by stochastic components and Monte Carlo simulation. Basically
only a DTM and a map of release areas is required to get started. This allows
its straightforward application in education. Additional information such as
spatially distributed friction coefficients derived from land cover maps are
easily added for scenario modeling. This allows for example the visualization
of the impact of protection forest decline on rockfall run-out length by
simulating scenarios with and without forest cover through the application of
different friction coefficients (see Table

The GPP model is an attempt to bundle the development efforts put into several geomorphological process models within recent years into a single free and open-source application. It is the author's opinion that making them available in a new and free implementation, even extended by new components, is important for geomorphological- and natural-hazards-related research and education. The modular structure of the framework and in particular of the source code facilitates the addition of further model approaches. The author is looking forward to contributions such as the extension of the framework through the addition of new modeling approaches or the implementation of accompanying SAGA tools, e.g., for automatic model parameter calibration based on observed events.

The SAGA source code repository, including the GPP
model, is hosted at

Alternatively, the source code and binaries can be downloaded directly from
the files section at

The data used for the examples shown in this paper are available as a supplementary zip folder.

The author would like to thank the Federal State of Vorarlberg for providing the remote sensing data sets, especially Peter Drexel (Landesvermessungsamt Feldkirch). Edited by: Lutz Gross Reviewed by: Gertraud Meißl and one anonymous referee