r.avaflow represents an innovative open-source computational tool for routing rapid mass flows, avalanches, or process chains from a defined release area down an arbitrary topography to a deposition area. In contrast to most existing computational tools, r.avaflow (i) employs a two-phase, interacting solid and fluid mixture model (Pudasaini, 2012); (ii) is suitable for modelling more or less complex process chains and interactions; (iii) explicitly considers both entrainment and stopping with deposition, i.e. the change of the basal topography; (iv) allows for the definition of multiple release masses, and/or hydrographs; and (v) serves with built-in functionalities for validation, parameter optimization, and sensitivity analysis. r.avaflow is freely available as a raster module of the GRASS GIS software, employing the programming languages Python and C along with the statistical software R. We exemplify the functionalities of r.avaflow by means of two sets of computational experiments: (1) generic process chains consisting in bulk mass and hydrograph release into a reservoir with entrainment of the dam and impact downstream; (2) the prehistoric Acheron rock avalanche, New Zealand. The simulation results are generally plausible for (1) and, after the optimization of two key parameters, reasonably in line with the corresponding observations for (2). However, we identify some potential to enhance the analytic and numerical concepts. Further, thorough parameter studies will be necessary in order to make r.avaflow fit for reliable forward simulations of possible future mass flow events.

Rapid flows or avalanches of snow, debris, rock, or ice, or processes, process chains, or process interactions involving more than one type of movement or material, frequently lead to loss of life, property, and infrastructures in mountainous areas worldwide. All state-of-the-art methods for anticipating the occurrence, characteristics, and dynamics of such events rely on computer simulations. On the one hand, models attempt to identify those areas where mass flows are likely to release (landslide susceptibility; Guzzetti, 2006; Van Westen et al., 2006). On the other hand, they attempt to anticipate the motion of rapid mass flows once they are released (Hungr et al., 2005a). Whilst conceptual models (Lied and Bakkehøi, 1980; Gamma, 2000; Wichmann and Becht, 2003; Horton et al., 2013; Mergili et al., 2015) are employed to identify possible impact areas at broad scales, physically based dynamic models are used for the detailed back-analysis or prediction of specific events.

Advanced fluid dynamics offer a broad array of physically based dynamic modelling approaches for mass flows, mostly referred to as granular avalanches or debris flows. Such models often centre on two-dimensional “shallow flow” equations, but they vary considerably among themselves in terms of their concept, complexity, and capacity to model specific types of phenomena. Voellmy (1955) pioneered mass flow modelling, followed by the work of Grigoriyan et al. (1967), Savage and Hutter (1989), Takahashi (1991), Iverson (1997), Pitman and Le (2005), and many others (see Pudasaini and Hutter, 2007 for a review). Savage and Hutter (1989) introduced depth-averaged mass and momentum conservation equations which were later utilized, modified, and extended by Mangeney et al. (2003, 2005), Denlinger and Iverson (2004), and McDougall and Hungr (2004, 2005). The Savage and Hutter (1989) model was further extended to include the effects of pore fluid by Iverson and Denlinger (2001), Savage and Iverson (2003), Pitman and Le (2005), Pudasaini et al. (2005), Pastor et al. (2009), and Hutter and Schneider (2010a, b). Still, these approaches either represent effectively one-phase models, or do not fully consider the two-phase nature of most mass flows. More recently, the software GeoClaw and its extension D-Claw consider shallow water and quasi-two-phase flows (M. J. Berger et al., 2011; Iverson and George, 2016). Pudasaini (2012) introduced a general two-phase mass flow model including several essentially new physical aspects of two-phase solid–fluid mixture flows. In comparison to one-phase models, amongst a few other two-phase approaches (e.g. Kowalski and McElwaine, 2013), this appears suitable for the realistic simulation of most types of process chains and interactions such as overtopping of a lake and a subsequent flood or debris flow due to the impact of a landslide into the lake.

Entrainment of the basal material into the flow may substantially alter the dynamics and characteristics of mass flows, increasing their destructive potential (Hungr and Evans, 2004, Hungr et al., 2005b; Reid et al., 2011; C. Berger et al., 2011; Pirulli and Pastor, 2012). Empirical laws for entrainment were proposed by Rickenmann et al. (2003), McDougall and Hungr (2005), and Chen et al. (2006), whereas mechanical concepts were introduced by Fraccarollo and Capart (2002), Pitman et al. (2003a), Sovilla et al. (2006), Medina et al. (2008), and Iverson (2012). The available entrainment models are effectively single phase and developed for bulk debris (Armanini et al., 2009; Crosta et al., 2009; Hungr and McDougall, 2009; Pirulli and Pastor, 2012). Whilst the importance of erosion and the associated change of the basal topography (Fraccarollo and Capart, 2002; Hungr and Evans, 2004; Hungr et al., 2005b; Le and Pitman, 2009) have been recognized by the scientific community, attempts to simulate deposition of mass flow material are sparsely documented.

Various types of numerical schemes have been used to solve mass flow model equations in order to redistribute mass and momentum (e.g. Davis, 1988; Toro, 1992; Nessyahu and Tadmor, 1990; Tai et al., 2002; Wang et al., 2004). Previously, equations were commonly formulated and solved for predefined types of topographies (Pudasaini et al., 2005, 2008; Wang et al., 2004), whereas a mathematically consistent application to arbitrary mountain topographies – and therefore to real-world conditions – still remains a challenge (Mergili et al., 2012). This issue is closely related to the fact that the model equations are commonly expressed in topography-following coordinates hardly compatible with global Cartesian coordinates, which usually appear in geographic information systems (GIS) and are referred to as GIS coordinates in the following. Nevertheless, some of the mass flow models mentioned have been implemented in computational tools used for hazard mapping and zoning, such as DAN (Hungr, 1995), TITAN2D (Pitman et al., 2003b; Pitman and Le, 2005), SamosAT (Sampl and Zwinger, 2004), or RAMMS (Christen et al., 2010a, b). Hergarten and Robl (2015) developed a modelling tool relying on the open-source flow solver GERRIS (Popinet, 2009).

None of these models explicitly consider stopping and deposition, and they offer only basic functionalities for simulating chains or interactions of two-phase mass flows. There is, however, a particular need to appropriately consider process chains and interactions in mass flow simulations: some of the most destructive events in history have evolved from cascading effects, such as the 1970 Huascarán event in Peru (Evans et al., 2009) or the 2002 Kolka–Karmadon event in Russia (Huggel et al., 2005).

The present work addresses some of the needs and issues raised by introducing the multifunctional open-source computational framework r.avaflow, employing an enhanced version of the Pudasaini (2012) two-phase flow model for routing mass flows from a defined release area down arbitrary topography to a deposition area. Next, we introduce the structure and components of r.avaflow (Sect. 2). Then, we perform two computational experiments in order to demonstrate the functionalities of the computational framework (Sect. 3). We discuss the implementation of r.avaflow and the implications of our findings (Sect. 4) and finally conclude with the key messages of the work and a brief outlook on the next steps (Sect. 5).

r.avaflow computes the propagation of mass flows from one or more given release areas over a defined basal topography until (i) all the material has stopped and deposited; (ii) all the material has left the area of interest; or (iii) a user-defined maximum simulation time has been reached. r.avaflow is developed along two lines with regard to its software environment and operation, r.avaflow [EXPERT] and r.avaflow [PROFESSIONAL]. The latter represents a stand-alone version with still reduced functionalities. It is operated through a graphical user interface (GUI), suitable for practitioners. The present work, however, refers to r.avaflow [EXPERT] which is implemented as a raster module of the open-source software package GRASS GIS 7 (Neteler and Mitasova, 2007; GRASS Development Team, 2016). We use the Python programming language for data management, preprocessing, and post-processing tasks (module r.avaflow). The flow propagation procedure (see Sect. 2.3 and 2.4) is written in the C programming language (sub-module r.avaflow.main). Together with Python, the R software environment for statistical computing and graphics (R Core Team, 2016) is employed for built-in validation and visualization functions. Figure 1 illustrates the logical framework of r.avaflow.

Multiple model runs may be executed in parallel, exploiting all computational cores available (see Sect. 2.5). This speeds up the processing considerably and allows the use of r.avaflow on computational clusters. Parallelization is implemented at the Python level (Mergili et al., 2014, 2015): for each model run, a batch file is produced within the module r.avaflow. This batch file calls the Python-based sub-module r.avaflow.mult, launching r.avaflow.main, which is then executed with the specific parameters for the associated model run. Thereby, the Python library “Threading”, a higher-level threading interface is exploited. The Python class “Queue” is employed for handling the queue of items to be processed.

r.avaflow was developed and tested with the operating systems (OS) Ubuntu
12.04 and 16.04

Experiments where parallel processing is not applied are performed on an
Intel^{®} Core i7 975 with 3.33 GHz and 16 GB
RAM (DDR3, PC3-1333 MHz), exploring a maximum of eight cores through
hyperthreading and using the OS Ubuntu 12.04

The key input parameters of r.avaflow are summarized in Table 1. Essentially, r.avaflow relies on (i) a digital terrain model (DTM) representing the elevation of the basal surface (in the release areas beneath the release mass) before the event under investigation, (ii) raster maps of the spatial distribution of the solid and fluid release heights or hydrographs of solid and fluid release, and (iii) a set of flow parameters (Table 2). Input raster maps of the entrainable solid and fluid heights, and a raster map or value defining the empirical entrainment coefficient (needed for entrainment) are optional. Instead of the solid and fluid release and entrainable heights, the total heights and fixed values of the solid concentration may be defined.

Logical framework of r.avaflow. The transformations and retransformations refer to the conversion of heights and GIS coordinates to depths and topography-following coordinates, and vice versa (see Sect. 2.3).

There is no restriction imposed on the arrangement of the release cells. With the term “cell”, we refer to a regular, equidistant, square, ground-projected computational/numerical unit, i.e. an element of a GIS raster. Patches of cells where the release height is larger than zero may be defined in various parts of the investigation area. An arbitrary number of release hydrographs – each associated with a given set of coordinates – can be defined alternatively or in addition to the release masses. This allows the simulation of complex interactions between different types of processes (see Sect. 3). Hydrographs are defined through their solid and fluid heights at the centre point of the hydrograph profiles, and by the solid and fluid flow velocities. The flow height distribution along the hydrograph profile – which should be aligned perpendicular to the main flow direction – is derived from the assumptions of a horizontal cross section of the flow table and a maximum profile length (Fig. 2).

Key input and output parameters of r.avaflow – s: solid; f: fluid;
t: total. Remarks: 1: mandatory; 2: one of the input data sets A, B, or
C

Flow parameters and entrainment coefficient required with the enhanced version of the Pudasaini (2012) two-phase flow model. Exp. 1 and 2 refer to the values used for the computational experiments introduced in Sect. 3.

Mandatory parameters further include the time interval at which output maps
are written

If a single model run is executed (see Fig. 1), the output of r.avaflow
consists in raster maps of solid, fluid, and total flow heights, flow
velocities in

Sketch of a hydrograph profile. The flow surface of input
hydrographs is defined by

The core functionality of r.avaflow consists in the redistribution of mass
and momentum, employing a dynamic flow model and a numerical scheme. Thereby,
the tool offers implementations (i) of a single-phase shallow water model
with Voellmy friction relation (Christen et al., 2010a, b; Fischer et
al., 2012) and (ii) essentially the Pudasaini (2012) two-phase flow model
with ambient drag (Kattel et al., 2016) and a set of additional numerical
treatments (complementary functions) outlined in Sect. 2.4. In the present
work, we only consider the implementation (ii). It builds on the conservation
of mass and momentum, computed separately but simultaneously for the solid
and fluid components of the flow. A system of six differential equations
(expressed in locally topography-following coordinates) represents the basis
for a set of six flux and source terms, regarding solid and fluid flow depths
(

The Pudasaini (2012) model employs the Mohr–Coulomb plasticity for the solid stress. The fluid stress is modelled as a solid-volume, fraction-gradient-enhanced, non-Newtonian viscous stress. The generalized interfacial momentum transfer includes viscous drag, buoyancy, and virtual mass induced by relative acceleration between the phases. A new generalized drag force is proposed that covers both solid-like and fluid-like contributions. Strong coupling between the solid-momentum and the fluid-momentum transfer leads to simultaneous deformation, mixing, and separation of the phases. Inclusion of the non-Newtonian viscous stresses is important in several aspects. The advection and diffusion of the solid volume fraction play an important role. The model includes a number of innovative, fundamentally new, and dominant physical aspects. Please consult Pudasaini (2012) for the full details of the model, including the corresponding equations. The flow parameters required are summarized in Table 2.

Solving the differential equations and propagating the flow from one cell to the next requires the implementation of a numerical scheme. For this purpose, r.avaflow employs a high-resolution total variation diminishing non-oscillatory central differencing (TVD-NOC) scheme, a numerical scheme used to avoid unphysical numerical oscillations (Nessyahu and Tadmor, 1990). Cell averages of all six state variables are computed using a staggered grid: the system is moved half of the cell size with every time step; the values at the corners of the cells and in the middle of the cells are computed alternatively at half and full time steps, respectively. The TVD-NOC scheme with the minmod limiter has successfully been applied to a large number of mass flow problems (Tai et al., 2002; Wang et al., 2004; Mergili et al., 2012; Pudasaini and Krautblatter, 2014; Kafle et al., 2016; Kattel et al., 2016).

The input and output of r.avaflow (see Sect. 2.2) is discretized on the basis
of GIS coordinates, i.e. in cells which are rectangular in shape in the
ground projection. For the numerical solution, the cell lengths in

Functionalities of r.avaflow introduced for numerical purposes (ID 1–3) or complementing the Pudasaini (2012) model (ID 4–5). Exp. 1 and 2 refer to the computational experiments introduced in Sect. 3; Y: activated, N: deactivated.

We note that all total (solid plus fluid) heights and depths represent the real-world heights and depths only if all the pores in the solid material are filled with fluid (pores filled with air are excluded).

Table 3 summarizes some additional functions of r.avaflow. The functions with ID 1–3 have been introduced to compensate for deficiencies of the numerical scheme and its implementation experienced with complex real-world flows (see Sect. 4). Entrainment and stopping, in contrast, represent dynamic functions not covered by the Pudasaini (2012) model and are executed at the end of each time step (see Fig. 1). Even though the separation of the complementary functions from the TVD-NOC scheme, and their treatment in a simple forward Euler manner, can be questioned physically and mathematically, we consider the current implementation a reasonable first approximation (see Sect. 4). We now elaborate the concepts employed for entrainment as well as for stopping and deposition in more detail.

Full handling of the evolution of the basal topography within the TVD-NOC
scheme is not straightforward and could also produce some diffusion.
Therefore, as entrainment is not included in the original Pudasaini
(2012) model, entrainment is treated as a complementary function in a first
step. We note, however, that the time steps at which entrainment and the
change of the basal topography are updated are identical to the time steps of
the numerical scheme. The potential solid and fluid entrainment rates

Interactions of the flow with the basal topography:

The changes in gravitational acceleration also influence the magnitude of the
frictional terms (Pudasaini and Hutter, 2003), which are important for
stopping processes. In the literature, few approaches explicitly consider
stopping processes directly in their numerical scheme by operator splitting
methods coupled with the determination of admissible stresses (e.g. Mangeney
et al., 2003; Zhai et al., 2015). Here, in order to consider stopping which
occurs at a spatial scale that is not numerically resolved, we choose a
different approach by proposing the dimensionless factor of mobility (FoM),
relating the distance required for stopping

FoM can relate to various spatial units, such as (i) a single cell; i.e. FoM
is computed separately for each cell (it may happen that stopping of the flow
occurs at a certain cell, but not at its neighbour cells); (ii)

The third possibility is currently implemented with r.avaflow as an optional
function. If activated, the simulation terminates as soon as stopping occurs
and the entire flow material is deposited. Note that, in the current
implementation, stopping and deposition always consider the total mass,
without differentiating between the solid and the fluid components. This
simplification is reasonable for flows characterized by a relatively small
fluid volume fraction. The change of basal topography due to entrainment

r.avaflow includes a built-in function to perform multiple model runs at a
time with controlled or random variation of uncertain input parameters
between given lower and upper thresholds. Essentially, this concerns the flow
parameters (see Table 2) but also the solid concentration of the release
mass

It facilitates multi-parameter sensitivity analysis and optimization efforts.

The results of all model runs are aggregated to an impact indicator index
(III) and a deposition indicator index (DII), each in the range 0–1. III
represents the fraction of model runs where

The model runs can be assigned to multiple computational cores (parallel processing), enabling the exploitation of high-performance computational environments (see Sect. 2.1).

Validation criteria used in r.avaflow (see also Fig. 4). S: single
model run, binary simulation result; M: multiple model runs, simulation
result in the range 0–1. The concepts of CSI and D2PC are taken from
Formetta et al. (2016). All validation parameters are computed for

Validation of r.avaflow results.

r.avaflow can be used to produce map layouts and animations of the key
results (see Fig. 1). It further includes built-in functions to validate the
model results against observations. Validation relies (i) on the availability
of a raster map of the observed impact or deposition area of the event under
investigation, (ii) on a user-defined profile along the main flow path (see
Table 1), or (iii) on measurements of

Values of

In contrast, ROC (receiver operating characteristic) curves are used to test
the performance of the overall output of multiple model runs. Such curves are
produced for III (OIA as reference) and/or DII (ODA as reference): the true
positive rate is plotted against the false positive rate for various levels
of III or DII. The area under the curve connecting the resulting points,
AUROC, is used as an indicator for model performance (AUROC

Further, the difference between observed and simulated values of

In a first step, the potential of r.avaflow for simulating process chains is
demonstrated, considering the interaction between one or more landslides, a
reservoir, and the dam impounding the reservoir. This experiment represents a
follow-up to the work of Pudasaini (2014), Kafle et al. (2016), and Kattel et
al. (2016). We construct a generic landscape of size

Landslides 1 and 2 consist of 75 % solid and 25 % fluid by volume (uniformly mixed); the input hydrograph I1 (see Fig. 5b) consists of 50 % solid and 50 % fluid per volume. The parameters and settings applied are summarized in Tables 2 and 3.

Three computational experiments are performed, with increasing complexity
from A to C:

Experiment 1A: Landslide 1 is released and interacts with the reservoir. The dam is assumed stable and may therefore not be entrained.

Experiment 1B: Again, Landslide 1 is released and interacts with the reservoir. However, dam material is allowed to be entrained in this experiment.

Experiment 1C: Landslide 2 is released and interacts with the dam and the
reservoir. The release from the input hydrograph I1 starts after 10

Generic landscape used for Experiment 1A–C.

All experiments are performed at a cell size of 10

Key results of Experiment 1A.

Key results of Experiment 1B.

Key results of Experiment 1C.

Animations illustrating the time evolution of the flow heights in all three experiments are enclosed in Animations 1A, B, and C in the Supplement.

Figure 6a–f illustrates the flow heights at selected points of time during
Experiment 1A. Landslide 1 (see Fig. 5a) impacts the backward portion of the
reservoir after few seconds and generates a water wave – oblique and
perpendicular to the impact – that overtops the dam from

Experiment 1B (Fig. 7) is identical to the Experiment 1A until the point when
the impact wave reaches the dam at

The temporal patterns of the simulated entrainment and wave propagation are
clearly reflected in the discharge recorded at the output hydrograph O1 (see
Fig. 7g). As a consequence of dam overtopping, fluid discharge at O1 starts
increasing at

In Experiment 1C (Fig. 8), Landslide 2 impacts the dam and the frontal part
of the reservoir less than 10

From

The Acheron rock avalanche in Canterbury, New Zealand (Fig. 9), occurred
approximately 1100 years BP (Smith et al., 2006). It is characterized by
sharp bending of the flow path, a limited degree of spreading into the
lateral valleys, and a high mobility (travel distance: 3550

We employ a 10 m resolution digital elevation model (DEM) derived by
stereo-matching of aerial photographs. ODA and OIA are derived from field and
imagery interpretation as well as from data published by Smith et al. (2006).
The OIA possibly underrepresents the real impact area, as it might exclude
some lateral and run-up areas of the rock avalanche which are not any more
recognizable as such in the field. The distribution of release and deposition
heights and an estimated release volume of

The Acheron rock avalanche.

Preliminary tests have shown that the simulation results of r.avaflow are
potentially sensitive to variations in the initial solid fraction

Experiment 2A: III and DII are computed from a set of
121 model runs. Thereby,

Experiment 2B: r.avaflow simulation with the optimized values of

Both experiments are conducted at a cell size of 20

Figure 10 illustrates III and DII derived with the parameter settings shown
in Tables 2 and 3 (Experiment 2A). AUROC is 0.830 with regard to III and
0.838 with regard to DII. In general, those areas with high values of III
coincide with the OIA, whilst those areas with lower values of III lie close
to the margins or outside of the OIA. The performance of III suffers from the
motion of small portions of the simulated avalanche in the wrong (northern)
direction and from excessive lateral spreading and run-up in the upper part,
observed for all tested combinations of

We now focus on the DII map and evaluate the performance of the deposition
maps simulated with the various combinations of

Results of Experiment 2A:

Validation and optimization of DII for the Acheron rock avalanche
(see Table 4 for the criteria):

Consequently, we consider

The key purpose of the present article is to provide a general introduction to the key functionalities of the computational tool r.avaflow. Thereby, the simulated patterns of flow height in Experiment 1 (see Sect. 3.1) are plausible, and the agreement of the observed and simulated deposition areas in Experiment 2B (see Sect. 3.2) appears reasonable. Yet, these experiments can neither replace model validation with observed process chains or interactions, nor can they replace thorough multi-parameter sensitivity analysis and optimization efforts, which will both be the subjects of future research. Fully documented two-phase process chains with readily available pre- and post-event DTMs are scarce. Preliminary r.avaflow results for the 2012 Santa Cruz multi-lake outburst flood in the Cordillera Blanca, Peru (Emmer et al., 2016), are however promising.

Results of Experiment 2B.

Experiment 2 serves for the demonstration of the parameter sensitivity analysis and optimization functions of r.avaflow. The outcomes may be different when changing the cell size or any of the flow parameter values (see Table 2). Making r.avaflow fit for forward predictions will require a thorough multi-parameter sensitivity analysis and optimization campaign involving a large number and variety of well-documented events. Thereby, we aim at obtaining guiding parameter values – or, more appropriately, guiding parameter ranges – for mass flow processes of different types and magnitudes. Approaches to perform such analyses are readily available, and some of them can be directly coupled to r.avaflow (Fischer, 2013; Fischer et al., 2015; Aaron et al., 2016; Krenn et al., 2016). However, due to the complex nature of two-phase mixture flows, r.avaflow depends on a relatively large number of flow parameters, a fact that represents a particular challenge in terms of the computational resources as well as in terms of visualization and interpretation of the results of multi-parameter studies.

r.avaflow represents a modular framework, allowing for the future enhancement of its particular components. One issue concerns the numerical implementation of the two-phase model equations, combining topography-following coordinates with the quadratic cells of the raster data given in GIS coordinates (see Sect. 2.3). As in comparable simulation tools (e.g. Christen et al., 2010a, b; Hergarten and Robl, 2015), approximations are currently used for coordinate transformation in r.avaflow. This issue is closely related to the fact that the model equations that are commonly expressed in topography-following coordinates are hardly compatible with the data given in GIS coordinates.

A detailed and fully discrete description of the TVD-NOC scheme exists in
the literature (Wang et al., 2004), and the scheme served well for various
theoretical test cases (e.g. Pudasaini et al., 2014; Kafle et al., 2016;
Kattel et al., 2016). However, we also identify two major drawbacks:

Although the numerical scheme itself should be shock capturing and volume preserving (Tai et al., 2002; Wang et al., 2004), these properties may not fully hold in practical applications (i.e. bounded gravitational mass flows with well-defined margins over complex topography). The complementary functions with ID 1–3 introduced in Sect. 2.4 partly compensate for the issues raised.

For real flow applications, full handling of the evolution of the basal topography is not straightforward: the TVD-NOC scheme may introduce diffusion even though the evolution of the basal topography is not a standard transport equation. Entrainment is therefore, as a first step, included as a complementary function.

The numerical scheme employed will have to be enhanced to directly and effectively incorporate the complementary functions outlined in Sect. 2.4 in a fully consistent way. Extensions of similar schemes have been tested for generic examples (e.g. Zhai et al., 2015) and could serve as a valuable basis also to implement a mechanical model for erosion, entrainment, and deposition (Pudasaini and Fischer, 2016). On the one hand, such an erosion model may build on existing concepts (e.g. Fraccarollo and Capart, 2002; Sovilla et al., 2006; Medina et al., 2008; Armanini et al., 2009; Crosta et al., 2009; Hungr and McDougall, 2009; Le and Pitman, 2009; Iverson, 2012; Pirulli and Pastor, 2012). On the other hand, it may further require some fundamentally new ideas with regard to deposition.

We have introduced r.avaflow, a multifunctional open-source GIS application for simulating two-phase mass flows, process chains, and interactions. The outcomes of two computational experiments have revealed that r.avaflow (i) has the capacity to simulate complex solid–fluid process interactions in a plausible way, and (ii) after the optimization of the basal friction angle and the solid content of the release mass, reasonably reproduces the observed deposition area of a documented rock avalanche. However, it was out of the scope of the present work to validate the results obtained for complex process interactions against observed real-world data or even to conduct a comprehensive multi-parameter optimization campaign. Such efforts will be the next step towards making r.avaflow ready for the forward prediction of possible future mass flow events. Thereby, we will attempt to establish guiding parameter values for different types of processes and process magnitudes.

At the same time, we have identified a certain potential for the future enhancement of some the components of r.avaflow. The key challenges will consist in (i) integrating the model equations in an up-to-date numerical scheme, allowing to directly include the complementary functions, and (ii) replacing the empirical entrainment model with a mechanical model for entrainment and deposition.

The model codes along with a user manual are available at

The scripts, the text file, and the GRASS locations with the spatial data
required for reproducing the computational experiments described in Sect. 3
are available at

The authors declare that they have no conflict of interest.

The work was conducted as part of the international cooperation project “A GIS simulation model for avalanche and debris flows (avaflow)” supported by the German Research Foundation (DFG, project no. PU 386/3-1) and the Austrian Science Fund (FWF, project no. I 1600-N30). We are grateful to Matthias Benedikt and Matthias Rauter for comprehensive technical support. Edited by: Simon Unterstrasser Reviewed by: J. K. Kowalski and one anonymous referee