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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
253
DOI: 10.4408/IJEGE.2011-03.B-030
TopFlowDF - A SIMPLE GIS BASED MODEL TO SIMULATE
DEBRIS-FLOW RUNOUT ON THE FAN
C
HRistian
SCHEIDL
(*)
& d
ieteR
RICKENMANN
(**)
(*)
University of Natural Resources and Applied Life Sciences, Vienna; Institute of Mountain Risk Engineering,
Peter Jordanstrasse 82, 1190 Vienna, Austria. Email: christian.scheidl@boku.ac.at (author for correspondence)
(**)
Swiss Federal Research Institute WSL, Zürcherstrasse III, 8903 Birmensdorf, Switzerland. Email: dieter.rickenmann@wsl.ch
INTRODUCTION
Throughout the world, debris flows endanger set-
tlements and infrastructures - often with disastrous ef-
fects for the affected communities. It is therefore not
surprising that the risk concept for natural hazards (e.g.
H
einimann
et alii, 1988; G
lade
& G
RozieR
, 2005) was
also extended to debris-flow processes within the last
decades (f
uCHs
et alii, 2008). Subsequently, this ap-
proach causes a demand for reliable debris-flow runout
prediction methods, especially when delineating haz-
ardous areas on the fan. To describe the depositional
characteristics and runout behaviour of debris flows,
several approaches, either based on empirical-statistical
or dynamical methods, have been developed during the
last decades. The complexity of prediction methods for
debris-flow runout on the fan vary from simple one-di-
mensional topographical approaches to two-dimension-
al numerical continuum models. An overview of recent
debris-flow runout models can be found in R
iCkenmann
,
2005; H
üRlimann
et alii 2008; s
CHeidl
& R
iCkenmann
,
2010 and R
iCkenmann
& s
CHeidl
, in press.
However, practical application, respectively the
selection of adequate runout prediction models, is
mainly based on their availability and on the require-
ments of local hazard assessments. In Austria for in-
stance, the criterion to delineate hazardous zones for
potential debris-flow events is based on the maximum
runout distance or maximum inundated area on the fan
(e.g. s
CHmid
, 2005). To investigate the similar spatial
relevant area in Switzerland, it is necessary to estimate
ABSTRACT
Typically runout prediction methods - either based
on empirical or on dynamical approaches - are applied
to delineate possible debris-flow inundation zones on
the fan for hazard mapping purposes. However, sev-
eral case studies indicate that empirical relations may
be valid only for situations which are similar to those
represented by the data used for their development,
and that a more accurate description of the debris-
flow depositional process requires dynamical param-
eters which are often not easily constrained. In this
study we propose that the topography of the potential
deposition area has a major influence in the runout of
a debris flow. We combine a random based flow al-
gorithm, generating a maximum simulation perimeter
on the fan, with the simple dynamical approach of a
constant discharge model to predict the maximum ru-
nout on the fan. The program called TopFlowDF sim-
ulates deposition zones, associated deposition heights
and a spatial distribution of the maximum flow veloc-
ities. The GIS-based simulation model runs with high
resolution (2.5 m x 2.5 m) digital elevation models,
generated for example from LiDAR data, and is tested
with debris-flow events from Switzerland and South
Tyrol. The predicted runout patterns of TopFlowDF
are further compared with the empirical runout pre-
diction method TopRunDF.
K
ey
words
: debris flow, predictive modelling, GIS
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C. SCHEIDL & D. RICkENMANN
254
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
For a constant flow-width, the linear runout distance
on the fan L
f
can analytically be estimated under consid-
eration of mass- and momentum-conservation, using:
with
Equation (1b) describes the driving component
of a debris flow mass, based on the flow velocity (v)
and the flow height (h) above the starting point of the
deposition (with the velocity at deposition v
d
and the
deposition height h
d
), as well as the mean angle of the
approach channel (θ
c
) and mean angle of the fan (θ
f
).
The resistance to flow is described by Eq. (1c) with the
friction slope (S
fric
) accounting only for sliding friction.
Resistance to flow approaches
Equation (1a) can only yield to plausible results
(positive L
f
), if the friction slope exceeds the average
mean angle on the fan (Eq. 2).
S
fric
= k
fric
tanθ
f
with k
fric
>1
Studies show that the frictional slope S
fric
is very close
to the mean angle of the fan θ
f
generated by debris flows.
Based on five Canadian debris-flow events, H
unGR
et alii (1984) found reasonable agreement between ob-
served runouts on the fan and those predicted by Eq.
(1a) by assuming a constant friction slope (S
fric
= tan 10°).
They obtained the flow parameters v and h from design
discharge by means of empirical equations.
Based on 14 debris-flow events at the Kamikami-
hori valley in Japan (o
kuda
& s
uwa
, 1984), R
iCken
-
mann
(2005) reported better predictions of L
f
with
S
fric
=
1.12 tanθ
f
instead of
S
fric
= tan 10°. He further found
reasonable predictions of runout length for twelve
Swiss debris-flow events of 1987 with
S
fric
= 1.08 tanθ
f
.
d’a
Gostino
et alii (2010) found a
k
fric
value of
1.072 based on investigations of six debris-flow
events in the Dolomites (Eastern Italian Alps).
R
iCkenmann
& s
CHeidl
(2010) found a signifi-
cant correlation between the friction slope S
fric
and the
average fan slope θ
f
. Based on observed debris-flow
runout distances in Northern Italy (South Tyrol) and
Switzerland, they proposed:
S
fric
= 1.29 sin θ
f
the maximal runout respectively lateral spreading and
the intensity (flow height, flow velocity), of the poten-
tial debris-flow event (BWW/BRP/BUWAL, 1997).
These examples may justify different approaches to
predict the mobility of debris-flow events.
In this study we present TopFlowDF, an uncom-
plex, GIS based model to simulate debris-flow ru-
nout on the fan. The delineation of deposition zones,
simulated with TopFlowDF, includes a physical and
empirical component since the model combines the
simple dynamical constant discharge model (H
unGR
et alii, 1984; t
akaHasHi
, 1991) with the flow paths
simulation, implemented in TopRunDF (s
CHeidl
&
R
iCkenmann
, 2010). The study further describes the
basic concepts and verifies respectively evaluates the
model against observed debris-flow events in Swit-
zerland and Northern Italy (South-Tyrol). The resist-
ance to flow parameters, obtained by several applica-
tions of the constant discharge model, are discussed
and further compared with back-calculated friction
parameters of TopFlowDF simulation results. Finally
we compare the results of TopFlowDF with results
of the empirical based runout model TopRunDF for
Swiss debris-flow events.
FRAMEWORK OF TOPFLOWDF MODEL
CONSTANT DISCHARGE MODEL
H
unGR
et alii (1984) and t
akaHasHi
(1991) de-
scribed a dynamical model to estimate the runout on
the fan (L
f
), based on the work of T
akaHasHi
& y
osHida
(1979). This one-dimensional model assumes a con-
stant discharge from upstream and that deposition starts
at the place where the channel abruptly levels out, it is
therefore also denoted as leading-edge model (v
an
d-
ine
, 1996; P
RoCHaska
et alii, 2008). The profile of such
a debris flow at time t and t+Δt is modelled by the trap-
ezoidal shape, shown in Fig. 1 (t
akaHasHi
, 1991).
Fig. 1 - Process of stoppage of forefront of a debris flow
(Takahashi, 1991); SP denotes the starting point
of the deposition, the flow parameters are de-
scribed in the text
(1a)
(1b)
(1c)
(2)
(3)
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TopFlowDF - A SIMPLE GIS BASED MODEL TO SIMULATE DEBRIS-FLOW RUNOUT ON THE FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
255
simulated maximum extent of B
perimeter
provides the
basis for the two-dimensional simulation of the final
flow-height and flow-velocity patterns in step two.
In the second step the approach of the constant
discharge model is applied in a differential form to
each individual flow path(i):
In Eq. (5) the driving component U of a debris-flow
mass and the resistance component G are calculated by
Eqs. (1b) and (1c). The resistance to flow is described
by a user defined friction coefficient (k
fric
) according to
Eq. (2). The maximum runout, for each individual flow
path(i) is then estimated from the predefined starting
point of the deposition (SP) assuming uniform discharge.
For this reason the input peak discharge (Q
p
) has to be
partitioned, related to the length of each individual flow
path(i) and probability of each overflowed cell p(cell
j
),
associated with the flow path(i). The sub-discharge,
Q
path(i)
with m the number of cells within each path(i) and
n the number of all flow paths, is then estimated by:
with
and
Knowing the uniform sub-discharge Q
path(i)
, a max-
imum runout distance for each flow path(i) is estimated
by means of Eq. (5), and is reached when the calcu-
lated flow velocity over time equals zero. Instead of a
constant friction slope, the user needs to define a fric-
tion coefficient (k
fric
; Eq. 2). This approach results in a
variable resistance to flow during simulation, depend-
ing on the slope gradient between the actual outflow-
and inflow-cell. It further prevents the flowing mass to
accelerate on the simulated fan. Therefore the highest
velocities exist at the starting point of the deposition
(simulation). The simulations of the deposition heights
are based on the distribution of the total volume in pro-
portion to the overflow probability p(cell
j
) of each cell.
As an example, Fig. 4 shows the predicted depo-
sition- and velocity-pattern for the 2005 debris-flow
event at the Glattbach - torrent in Switzerland.
FLOw ROUTING ALGORITHM
The two-dimensional runout model TopFlowDF
combines the simple physical approach of the constant
discharge model with a random based flow algorithm
which is also implemented in the empirical runout predic-
tion model TopRunDF (s
CHeidl
& R
iCkenmann
, 2010).
In a first step, TopFlowDF automatically esti-
mates the maximum extent of the simulation perim-
eter B
perimeter
due to topographical conditions. The
quantity of this simulation perimeter is derived by
an area-volume relation, which was first proposed by
i
veRson
et alii (1998) to delineate lahar-inundation
hazard zones. B
perimeter
is estimated with a user defined
mobility coefficient k
B
(e.g. s
CHeidl
& R
iCkenmann
,
2010) and a debris-flow event volume V.
B
perimeter
= k
B
V
2/3
Based on the topography and the maximum ex-
pected areal extent (B
perimeter
), TopFlowDF simulates
lateral flow patterns by using a D8 single flow-al-
gorithm combined with a Monte Carlo technique as
described in H
üRlimann
et alii (2008) and s
CHeidl
&
R
iCkenmann
(2010). Figure 3 illustrates the effect of
lateral enlargement of the simulation perimeter, which
is based on multiple (n) individual flow paths(i) with
constant flow width b (= gridsize of the input DTM)
and a probability p(cell
j
) of each overflowed cell
within each flow path(i). Terminal conditions for the
individual flow pathways are set by the perimeter of
the elevation model or by adverse slopes.
The input parameters of the first step of Top-
FlowDF consist of a debris-flow volume, a mobil-
ity coefficient, a starting point of the deposition (fan
apex) and a digital terrain model of the fan area. The
(4)
Fig. 3 - Estimation of the simulation perimeter with multi-
ple individual flow pathways. SP denotes the user
defined start point
(5)
(8)
(7)
(6)
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C. SCHEIDL & D. RICkENMANN
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The flow parameters at the fan apex, for the example
in Fig. 4, are estimated with v = 8.84 m/s and h = 1.01 m
based on the observed Volume (V = 8,800 m
3
). The mean
angle of the fan respectively channel are θ
f
= 8.40 (S
f
=
0.15) and θ
c
= 20.72 (S
c
= 0.38). The analytical solution
of the runout distance for the Glattbach debris-flow event
results to 367 m, based on a friction slope of S
fric
= 0.17.
With a selected time interval of Δt = 0.5 s the differential
solution stops the debris-flow after 80 seconds reaching
a distance of 360 meters. With a smaller time interval,
Δt = 0.01, the estimated distance reaches 367 m (in
80 s). The differential approach shows more precise
results if we use smaller timesteps. Therefore, Top-
FlowDF uses a pre-defined time interval of Δt = 0.01.
The input parameters for the second step of Top-
FlowDF consist of peak discharge, flow-height and
flow-width as well as average channel slope above the
starting point and a friction coefficient.
For the simulations within this study, peak dis-
charge Q
p
and flow height h were estimated with em-
pirical equations proposed by R
iCkenmann
(1999):
The flow width b at the starting point as well as
the average channel slope S
c
were measured directly
from the LiDAR DTM, areal photographs and on
1:25,000 scale topographic maps.
TopFlowDF runs with high resolution (2.5 m x
2.5 m) digital elevation models, written in VB.NET
©
.
The executable program as well as the source-code
can be downloaded for free, after registration from
www.debris-flow.at
ANALYSIS OF RESULTS
To test the dynamical approach of TopFlowDF,
we compared the analytical (Eq. 1a) and differential
(Eq. 5) solutions of the constant discharge model for
an observed Swiss debris-flow event at the Glattbach
torrent in 2005 (Figure 5).
Fig. 4 - Simulation results of TopFlowDF for the Glattbach debris-flow event. a) predicted deposition zones, b) predicted
velocity pattern. SP denotes the starting point of the simulation Contour interval is 1 m
(12)
(11)
(10)
Fig. 5 - Comparison between analytical (Eq. 1a) and dif-
ferential (Eq. 5) solution of the constant discharge
model for the observed debris-flow event at the
Glattbach (Switzerland)
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TopFlowDF - A SIMPLE GIS BASED MODEL TO SIMULATE DEBRIS-FLOW RUNOUT ON THE FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
257
For this study, the runout on the fan of 14 debris-
flow events in Switzerland and 6 debris-flow events
in South Tyrol were simulated and evaluated with the
observed deposition patterns. For the modelling of the
individual simulation perimeters a back-calculated
mobility coefficient (k
Bobs
) is used, based on the ob-
served deposition area (B
obs
) and the observed event
volume (V
obs
) (s
CHeidl
and
R
iCkenmann
, 2010).
k
Bobs
= B
obs
/V
obs
2/3
Table 1 lists the used input parameters for all Top-
FlowDF simulations in this study.
Analysis of a large Swiss debris-flow event in the
Varuna catchment, with a total volume of 214,000 m
3
, an
upper limit of 50,000 m
3
for a single-surge volume was
estimated in relation to the documented peak discharge
(VAW, 1992). We therefore limited the “input-volume”
to 50,000 m
3
for the simulation procedure for debris-
flow events exceeding a total volume of 50,000 m
3
. This
concerned the debris-flow events at the Rotlauibach,
Saasbach and Seefeldbach, marked with a * in Table 1.
The following evaluation concept of TopFlowDF
is based on a methodology used in s
CHeidl
& R
iCken
-
mann
(2010) and first described by C
aRRanza
& C
as
-
tRo
(2006). Three different area-accuracies (denoted
as α, β and γ) are determined, based on the relations:
Similar the positive (ε) and negative (φ) volume-
prediction accuracies are defined. Here ε is defined as
the relation of the total volume within the predicted
deposition zones related to the observed deposition
areas, and φ is defined as the inverse value of the posi-
tive volume-prediction accuracy. The overall evalua-
tion factor (Ω) is then calculated as:
Ω = α - β - γ + ε
within a range of -2 ≤ Ω ≥ 2.
The best fit simulation is characterized by Ω = 2,
then the simulated deposition pattern equal the ob-
served deposition pattern. On the contrary, a value of
Ω = -2 implies no overlapping between the simulated
and observed deposition area.
(13)
Tab. 1 - Input process parameters for the TopFlowDF simulations of observed debris-flow events in Switzerland (CH) and
South-Tyrol (ST)
(9)
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C. SCHEIDL & D. RICkENMANN
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
Tab. 2 - Accuracies and adapted friction coefficients for the simulated debris-flow events with TopFlowDF. The possible range
of Ω is [-2,2]; SD denotes standard deviation,CH is for Swiss debris-flow events, whereas ST stands for South-
Tyrolean (Italy) debris-flow events
Fig. 6 - Comparison of ob-
served
deposition
areas and predicted
deposition
zones
with
TopFlowDF
a) Glattbach, b)
Schwendibach,
c)
Blauseeligraben, d)
Piz Caral, e) Heu-
gandtal f) Richleren,
g) Rotlauibach, h),
Gonerli, i) Brich-
boden, j) Val Mera
1. SP denotes the
starting point of the
deposition. Contour-
interval is 1 m
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TopFlowDF - A SIMPLE GIS BASED MODEL TO SIMULATE DEBRIS-FLOW RUNOUT ON THE FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
259
Therefore, starting flow parameters - flow-height,
maximum discharge as well as flow width - need to
be estimated based on empirical relations or on field
data. Further, a suitable coefficient for k
fric
of the fric-
tion slope in Equation 2 has to be selected, based on
a correlation between the friction slope S
fric
and the
fan slope S
f
. The existence of such a correlation can
be explained by rheological characteristics of debris-
flow events. Studies of J
aCkson
et alii (1987), m
aRCHi
& t
eCCa
(1995), C
Hau
et alii (2000) and R
iCkenmann
(2005) imply that granular flow behavior will lead to
a higher roughness and friction during depositional
flow, resulting in steeper fan slopes on average and
in a smaller mobility. A more viscous or muddy flow
behaviour, on the other hand, shows higher mobility
and results in smoother and flatter fans. However,
the back-simulated friction coefficients in this study
(k
fric(sim)
) are based on a reach wise estimation of the
resistance to flow during deposition of 14 debris-flow
events. Future back-simulations are necessary to test
The simulation results of the back-calculated de-
bris-flow events used for this study are shown in Figs.
6 and 7. If the simulated deposition area differed from
the observed deposition area (agreement of surface
area), the pre-defined friction coefficient was adapted
(k
fric(sim)
, Eq.2) until the simulated zones equalled to the
observed deposition area. The accuracies as well as
the best-fit k
fric(sim)
values are listed in Table 2.
On average, and for all used debris-flow events in
this study, TopFlowDF predicted 63 % of the observed
area and 76 % of the observed volume, compared to
the observed deposition zones. 37 % of the area and
24 % of the volume were predicted outside the ob-
served deposition zones. The average friction coeffi-
cient amounts to 1.070 +/- 0.044.
DISCUSSION AND CONCLUDING REMARKS
TopFlowDF simulates the maximum flow veloci-
ties and maximum deposition heights on the fan, based
on the constant discharge approach (Equations 1a-1c).
Fig. 7 - Comparison of observed deposition areas and predicted deposition zones with TopFlowDF a) Gerental 3B, b)
Saasbach, c) Ri di Gallinoso, d) klammbach, e) Ri di Sozz; f) Draunbergerbach, g) Fanatjoch, h) koglbach, i)
Seefeldbach, j) Arundakopfbach. SP denotes the starting point of the deposition. Contour-interval is 1 m
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the difference between a reach wise estimation (as im-
plemented in TopFlowDF) of the friction coefficient
and a resistance coefficient, which is constant along
the entire flow path on the fan, as used together with
the analytical solution in Equation 1a.
Since the lateral spreading of the simulation perim-
eter B
perimeter
is controlled by the same approach as ap-
plied in TopRunDF, the presented model TopFlowDF
behaves similarly, regarding the selection of a starting
point of the simulation and the use of the Monte-Carlo-
Iteration number (MCI). The starting point corresponds
to a single DTM cell within a cross-section of the chan-
nel close to the fan apex and is sensitive to the level of
detail of the digital terrain model. Using LiDAR data
with an orthogonal gridsize of 2.5 m a maximum differ-
ence of 10 m was determined between the user defined
start point and the observed start point of the deposition
for the simulated debris-flow events in this study.
s
CHeidl
& R
iCkenmann
(2009) found an opti-
mised iteration number MCI = 50, based on 14 simu-
lations of Swiss debris-flow events. This number was
also used for the simulation in this study. A detailed
discussion of the MCI number and its influence on the
simulation results is given in s
CHeidl
& R
iCkenmann
(2010) and R
iCkenmann
& s
CHeidl
(2010).
For large debris-flows, material may be deposited
on the fan outside of the main channel. In such a case
TopFlowDF is capable to estimate lateral runout on
the fan. In contrast to the similar two-dimensional
model TopRunDF (s
CHeidl
& R
iCkenmann
, 2010),
TopFlowDF is not only based on an empirical ap-
proach but include also a simple dynamical runout
model. Hence, higher uncertainties of the simulation
results of TopFlowDF may originate from the selec-
tion of input flow parameters and due to the separation
of the start momentum into multiple flow paths.
Comparing the simulation results of TopFlowDF
with TopRunDF (s
CHeidl
& R
iCkenmann
, 2010) a larg-
er standard deviation of the resulting accuracies and
a lower average overall evaluation factor (Ω) for the
results with TopFlowDF are noticed. Table 3 lists all
area- and volume-accuracies as well as the total evalu-
ation factors for the simulation results of TopFlowDF
and TopRunDF respectively, for the 14 Swiss debris-
flow events used in s
CHeidl
& R
iCkenmann
(2010). It
appears that for most of the debris-flow events simu-
lated with TopRunDF, more accurate results can be
achieved, compared to the simulation results of Top-
FlowDF. However, the difference between the mean
values of Ω and Ω* remains small, compared to its
possible range between -2 to 2. Moreover, the qual-
ity of the visual evaluation of the predicted deposition
zones of TopFlowDF compared to the observed depo-
sition areas (Figures 6 and 7) appears to be similar.
Tab. 3 - Comparison of TopFlowDF and TopRunDF based on the accuracies of predicted deposition zones.The results based
on TopRunDF (S
cheiDl
& r
icKeNmANN
, 2010) are denoted with *
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TopFlowDF - A SIMPLE GIS BASED MODEL TO SIMULATE DEBRIS-FLOW RUNOUT ON THE FAN
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
261
zano provided data about debris-flow events in South
Tyrol. Markus Zimmermann provided the original
maps which document the debris-flow events of 1987
in Switzerland. The Swiss Federal Office of Topog-
raphy (swisstopo) provided the LiDAR DTM for the
simulations of this study, which are based on DTM-
AV and DOM-AV ©2008 swisstopo (DV033492.2).
ACKNOWLEDGEMENTS
This study was funded by the Austrian Science
Fund (FWF) project no. L 180-N10 on “Runout pre-
diction of debris flows”. The Swiss Federal Office for
the Environment (FOEN) supported the documenta-
tion and analysis of the debris-flow events 2005 in
Switzerland. The Department 30 - Hydraulic Engi-
neering of the Autonomous Province of Bozen - Bol-
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