A detailed comparison between the performances of two different approaches to debris flow modelling was carried out. In particular, the results of a mono-phase Bingham model (FLO-2D) and that of a two-phase model (TRENT-2D) obtained from a blind test were compared. As a benchmark test the catastrophic event of 1 October 2009 which struck Sicily causing several fatalities and damage was chosen. The predicted temporal evolution of several parameters of the debris flow (such as flow depth and propagation velocity) was analysed in order to investigate the advantages and disadvantages of the two models in reproducing the global dynamics of the event. An analysis between the models' results with survey data have been carried out, not only for the determination of statistical indicators of prediction accuracy, but also for the application of the Receiver Operator Characteristic (ROC) approach. Provided that the proper rheological parameters and boundary conditions are assigned, both models seem capable of reproducing the inundation areas in a reasonably accurate way. However, the main differences in the application rely on the choice of such rheological parameters. Indeed, within the more user-friendly FLO-2D model the tuning of the parameters must be done empirically, with no evidence of the physics of the phenomena. On the other hand, for the TRENT-2D the parameters are physically based and can be estimated from the properties of the solid material, thus reproducing more reliable results. A second important difference between the two models is that in the first method the debris flow is treated as a homogeneous flow, in which the total mass is kept constant from its initiation in the upper part of the basin to the deposition in a debris fan. In contrast, the second approach is suited to reproduce the erosion and deposition processes and the displaced mass can be directly related to the rainfall event. Application of both models in a highly urbanized area reveals the limitation of numerical simulation which is inadequate in describing some disturbances of the flows that occurred during the alluvial event (e.g. the cars, the volume of debris within buildings etc.) which have a crucial influence on the evaluation of the maximum and final flow depths.

Debris flow occurrences are among natural phenomena which still produce damage and fatalities. Therefore in the last decades many efforts have been put in place to develop models able to simulate numerically the debris flow propagation, aiming at producing reliable hazard maps. It is possible to find several propagation models applicable to hyperconcentrated flows, which mainly differ for the adopted rheological schemes. In particular, they can be separated into single-phase models and two-phase models. Single-phase models assume that a debris flow acts as a homogeneous Bingham fluid composed of a mixture of water and sediment. From a rheological view point, such a mixture can be described by Herschel–Bulkley or even more complex models as, for example, that described by a quadratic law which assumes that the total friction stresses can be divided into different terms: yield stresses, viscosity stresses and turbulent–dispersive stresses; all of them being functions of the sediment concentration in the mixture. In any case, the hypothesis of the Binghamian nature of the fluid is necessary in order to simulate the arrest of the flow.

When the debris flows are treated as a two-phase model, the exchange
of mass between the erodible bed and the flow is taken into account as
well. The fundamentals of such models were first developed by

In particular, it has been noticed that the first type of model is more suitable for cases characterized by fine sediments, when the viscous shear rate is high. The second type of model is more suitable in cases in which the viscosity of the interstitial fluid is negligible and the solid fraction is composed of coarser material, so that the inertial shear rate acts predominately due to the collisions between gravels.

Furthermore, as was stressed by

In order to understand the real behaviour of the
propagation of a debris flow on a large scale, a real catastrophic
debris flow event was analysed by means of two different models:
the FLO-2D

The FLO-2D model is a propagation code for analysing debris flow dynamics widely adopted by researchers and
practitioners. Indeed, it is easy to find in the literature several applications of such a model, which mainly
differ in relation to the sediment characteristics, and hence, in relation to the adopted rheological parameters (see, for example,

In order to highlight the relative advantages and disadvantages of the two methodologies, they have been applied to a real complex case – namely, the alluvial event of 1 October 2009 which struck Messina Province (Italy) causing 37 fatalities and damage to public and private buildings and infrastructure. In particular, several debris flows in Giampilieri village, which was affected the most during the alluvial event, were simulated.

The paper is organized as follows: Sect. 2 presents a brief description of the two models; Sect. 3 describes the case study; Sect. 4 presents the boundary conditions along with data adopted as input for the two models; Sect. 5 reports the performed simulations; Sect. 6 shows the application of the ROC procedure to the case being. The paper ends with some conclusions about the main strengths and weaknesses of the two codes.

As mentioned before, the adopted models are based on depth-integrated
flow equations, though they differ in the mathematical descriptions
of the phenomenon. Indeed, the FLO-2D model, which is not fully
two-dimensional, is based on a monophasic Bingham scheme, modelled
through the quadratic rheological law developed by

FLO-2D is a commercial code developed by

The surface topography is discretized into uniform square grid
elements. In order to solve the momentum equation the FLO-2D
considers, for each cell, eight potential flow directions. Each
velocity computation is essentially one-dimensional and solved
independently from the other seven directions, so

The total friction slope

TRENT-2D is a code developed by

During the night of 1 October 2009 a heavy rainfall struck the Province of Messina
causing 37 fatalities and several damage to public and
private structures. This area located along the coast is characterized
by the presence of the Peloritan Arc, which determines a particular
morphology characterized by narrow river valleys with high hillslope
angles (within a range of 30–60

Map of Northeast Sicily struck by the debris flow on 1 October 2009.

Orthophoto of Giampilieri village:

In order to model the debris flows, three principal data sets are
needed: a digital terrain model (DTM), hydrological data, and
rheological properties of the sediment–water mixture. While the first
two data sets are the same for the two models, the rheological
properties are very different. The geometry inputs consist in the
definition of a flood plain area.
LIDAR data characterized by a spatial resolution of eight points per square metre were adopted for the
construction of the DTM. Moreover, for the urbanized area further elevation data were acquired on purpose through a theodolite.
The different grid systems implemented by
FLO-2D model and by TRENT-2D model were designed in such a way
that a grid of square cells with cell size

Regarding the hydrological input, the hydrological inputs relative to
the three mentioned data sets were considered. The same input hydrograph was used for both FLO-2D and TRENT-2D simulations; the
rate of water discharge corresponds to a rainfall of a 300-

It should be noted that in general the upstream input discharge

The debris flow discharge was determined by applying equation (

While for the Puntale and Loco creeks only one hydrological input was
considered, for the Sopra Urno Basin three inputs were
implemented. Such an assumption relies on the observed event dynamics
and from the analysis of the orthophoto gathered just after the event,
in which it is easy to distinguish the three sub-catchments. Also, it
was assumed that the debris flows that originated from the three
sub-catchments did not develop at the same time, but were separated from each
other by 6

Regarding the rheological parameters, the FLO-2D model relies on empirical parameters, while the TRENT-2D parameters have a more specific physical meaning.

The mono-phase modelling approach suffers from a need for calibration
with historical data, while a more physically based model, such as
the adopted two-phase one, is easier to apply. Indeed in
order to perform the simulations with the FLO-2D model, the
coefficients

Table

Input data of the hydrograph and rheology adopted for FLO-2D and TRENT-2D simulations.
For the FLO-2D: solid concentration in the mixture

Input liquid hydrographs assumed for triggering debris flows in FLO-2D and TRENT-2D simulations for Loco Basin, Sopra Urno Basin and Puntale Basin.

Regarding the simulation performed by the FLO-2D, a reconstruction of
the inundated area was obtained as output of the model. It is easy to recognize the portion of the urbanized area
affected by the debris flow, which fits fairly well with the surveys
conducted just after the event. The maximum flow depths during the
event obtained from the FLO-2D simulation are presented in
Fig.

Scenarios simulated with the FLO-2D (hydraulic discharge relative to 300-year return period; rheological parameters:

As regards the simulation performed by TRENT-2D, the maximum flow
depths reached during the simulations of the event are shown in
Fig.

Scenarios simulated with the TRENT-2D (hydraulic discharge relative to 300-year return period; rheological
parameters:

Measured and predicted values of maximum flow depth (

The results of both FLO-2D and TRENT-2D were compared with the
data gathered from on-site investigations, i.e. videos recorded during
the event and measurements of the depth of the sediment deposition
gathered just after the event. For example in Fig.

Evidence on the wall of the maximum depth observed during the event.

In particular, two field data sets are available: the values of the maximum
flow depth reached during the event (

Regarding maximum flow depths (

Predicted values obtained from FLO-2D simulations are smaller than
survey data, perhaps due to the value of the viscosity parameter
assumed and also the absence of anthropic features in the simulated
scenario, such as cars along the streets, which during the event
influenced the flow to a large extent. Looking at the TRENT-2D
results, predicted final depositions are smaller than those
measured. As for the flow heights, results are better in the main
streets and less accurate in the lateral narrow ones. TRENT-2D is a movable bed model and, hence, allows the erosion
caused by the debris flow propagation to be estimated. For the present case study, the maximum scour caused by bed
erosion was about 2–3 m. This estimate is in accordance with the scour data collected after the debris flow event (see Fig.

Orthophoto of Giampilieri urban area with positions where data of maximum flow depths and final sediment deposits are available from site surveys.

Considering the maximum velocities (

Although no field measures of debris flow velocities are directly available for the event here considered, the application of the formula proposed by

In order to have a clearer view of the error distribution
inside the flooded area, Fig.

Finally, some statistical analysis on the models performances have been conducted. The mean absolute error and the root mean square error have been determined for each model, as 1.2 and 1.5 respectively for the FLO-2D and 0.9 and 1.2 for the TRENT-2D.

Giampilieri village map indicating with coloured dots the prediction
error [%] for

In order to compare, not only by means of simple statistical
indicators, the results obtained by the two debris flow models, the
Receiver Operator Characteristic (ROC) approach was applied. Such
a method was originally developed to assess the performance of models
in signal detection theory and then applied in different fields such
as epidemiology, weather forecasting, machine learning and landslide
susceptibility

In a ROC graph the true positive rate (Sensitivity) is plotted vs. the
false positive rate (Specificity) for a cut-off point. The
sensitivity and the specificity are determined as follows:

A point in the ROC graph represents a sensitivity/specificity pair
corresponding to a particular decision threshold. A test with perfect
discrimination is located in the ROC graph in the upper left corner
(100

In this framework the ROC approach was applied in order to
evaluate the prediction of the two debris flow propagation models. The
ROC graph was determined for a cut-off value of
1.0

ROC graph related to a threshold value of 1.0 m, evaluating the performances of FLO-2D model and TRENT-2D model in prediction of the maximum flow depth.

The simulation of the alluvial event of 1 October 2009 in Giampilieri
was reproduced by means of two different models: the
FLO-2D

Street of Giampilieri village after the alluvial event of 1 October 2009. Case where the deposit material level has been influence by cars.

Finally, FLO-2D velocities are generally higher than those predicted by TRENT-2D, due to the different rheological models. It is important to point out that accurate representation of the topography in the grid system is an essential step to obtain a reasonable replication of the observed deposition patterns. A more detailed spatial resolution of floodplain strongly improves the model results. Moreover, results may also improve if the effects of flow obstructions, such as buildings, is incorporated into the model in a proper way. Possible explanations for the inaccuracy of the model results include both systematic topographic errors or the simplification of the real multi-surge event by a single triangular hydrograph. Bed level changes either between successive surges or at the base of a flow within one surge may cause a local change in the direction of the flow. A comparative analysis of the models results (FLO-2D and TRENT-2D) has shown that the TRENT-2D model is more accurate than the FLO-2D, although the simulation is affected by a distortion effect in evaluating the flow depth in the region of the flood area far from the main path. The determination of some statistical indicators indicates that TRENT-2D prediction is more accurate if compared with the one of the FLO-2D. Moreover, the application of the ROC approach confirms a general higher accuracy and precision of both models adopted for the simulation of the Giampilieri event, although a slightly higher sensitivity level is determined in the case of the FLO-2D when compared with TRENT-2D. Finally it can be stated that both models are good in the reproduction of the flooded area. In producing hazard and risk mapping, however, the FLO-2D is more user friendly while the TRENT-2D is more accurate.

All consultants of the OPCM 10 October 2009 no. 3815 are greatly acknowledged for the support demonstrated and for the useful information provided. We would like to thank the Public Civil Engineering Works Office of Messina and the Department of Civil Defence of the Sicilian Region for providing important data. Edited by: T. Glade Reviewed by: two anonymous referees